5,965 reputation
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bio website math.mit.edu/~shor
location Cambridge, MA
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visits member for 4 years, 7 months
seen 15 hours ago

Jun
3
answered What happens as you approach/cross the Planck temperature?
May
23
comment Quantum mechanics not in $L_2$-space
Isn't Hilbert space essentially $L_2$ by definition? Are you thinking of Banach spaces?
May
20
comment Find Eigenstates of a Hamiltonian that lets two spin 1/2 interact but also acts on one of them
The fact that $\sigma_{1z} \otimes \sigma_{2z}$ commutes with the Hamiltonian, as I mentioned above, can indeed be used to simplify the calculations.
May
20
comment Free-falling from rest into a Kerr black hole
Hi John ... never mind; I made a stupid mistake.
May
19
comment Free-falling from rest into a Kerr black hole
Just looking at these equations, doesn't $dt/d\tau$ become infinite at a radius larger than $r_s$? What does that mean?
May
19
comment Find Eigenstates of a Hamiltonian that lets two spin 1/2 interact but also acts on one of them
The first term that @Meng Cheng is talking about has been edited out. I have no idea whether your calculations are correct or not; if you did them right (where the first term is not squared), they should be.
May
19
comment Find Eigenstates of a Hamiltonian that lets two spin 1/2 interact but also acts on one of them
Doesn't $\sigma_{1z} \otimes \sigma_{2z}$ commute with the Hamiltonian?
May
19
comment What is the difference between general measurement and projective measurement?
@Sattwik: when they say "... it turns out that there are important problems such as the optimal way to distinguish a set of quantum states", they are talking about a problem that can be solved using only POVMs.
May
18
comment The virtual particles are only a fictive tool in equations? DO they exist or DON'T? And if they exist, why do we call them VIRTUAL?
@ACuriousMind: you realize that this is the Feynman diagram equivalent of the "shut up and calculate interpretation" of quantum mechanics. Telling people they're not supposed to think is always a bad idea.
May
17
comment What is the difference between general measurement and projective measurement?
Generalized measurements were used in this paper of Peres and Wootters, which is very important historically because thinking about its consequences led to the discovery of teleportation.
May
17
comment What is the difference between general measurement and projective measurement?
A POVM is a special case of general measurements where the measurement operators are not orthogonal projectors. You should figure out how POVMs are a special case of general measurements (the different outcomes are taken to orthogonal states, but the operators don't have to be projectors), and you should get more insight.
May
11
comment What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?
@CuriousOne: the physical prediction of anyons is not based solely on symmetry/algebra, but also on the fact that no other explanation is known for the fractional quantum Hall effect. Experimentalists are currently trying to provide conclusive evidence for the presence of non-abelian anyons in FQHE systems, and I am reasonably sure that they will do so within the next few years.
May
11
comment Would a collision of two black holes emit any electromagnetic radiation?
@CuriousOne: my impression is that the collision of two black holes occurs in a regime that is so far from the Planck scale that we can just ignore quantum effects. That is, the only emitted radiation would be gravitational radiation. But maybe we should wait until somebody who knows what they are talking about answers the question.
May
11
revised Where does the angular momentum of the solar system come from?
added 449 characters in body
May
11
comment What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?
@CuriousOne: If you don't believe anyons exist in nature, do you have an alternate explanation for the fractional quantum Hall effect?
May
11
answered Where does the angular momentum of the solar system come from?
May
11
comment What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?
If there are no solutions satisfying the pentagon and hexagon identities, then there is no theory of anyons for that fusion rule. If there are solutions, but the matrices are not unitary for any solution (this happens), then there is no physical theory of anyons for that fusion rule. Most fusion rules you could write down don't have corresponding anyons.
May
9
comment Free-falling from rest into a Kerr black hole
What do you think would happen to an object dropped into a black hole from infinity if it didn't enter the ergosphere?
Apr
9
comment Why does red light travel faster than blue light?
@Jon: Right. (Bangs head.) I meant refraction.
Apr
3
comment Do quasiparticles have antiparticles?
Some quasiparticles have antiparticles, and some quasiparticles act as their own antiparticles, just like ordinary particles. Charged quasiparticles will have antiparticles with opposite charge; uncharged quasiparticles may or may not be their own antiparticles.