116,202 reputation
7180347
bio website motls.blogspot.com
location Czech Republic
age 41
visits member for 4 years, 7 months
seen 20 hours ago

Hi, I am a string theorist and a publicist.


May
25
comment Conservation law of energy and Big Bang?
Dear @Dan, it is not a language game and you can only stand by your position if you're either blinded or unable to follow elementary arguments. On the other hand, you're right that the most sensible definition of energy is that it is a quantity that is conserved as a result of the time-translational invariance. However, what I am explaining to you is that there is no (conserved) energy in GR - obviously, the symmetry isn't there either. It's like the only sensible definition of a cold fusion reactor is a fusion reactor that is cold - but this doesn't imply that it actually exists. ;-)
May
25
answered How does non-commutativity lead to uncertainty?
May
25
comment Can the entropy density of a spacelike singularity arbitrarily exceed the inverse Planck volume?
This is a nice question I would like to be answered, too. In some moral sense, it must be true that the Planckian entropy density is a limit - holography makes the maximum volume density much smaller for bigger-than-Planckian volumes and smaller volumes "don't physically exist", in a sense - but I don't know whether it can be demonstrated by some argument, whether it implies the Hartle-Hawking-like unique state at the beginning of the Big Bang, and/or a unique final state in the black hole singularity.
May
24
answered A question on an assumption of space-time
May
24
comment state vector notation
$\langle x|y\rangle$ is what mathematicians would write as $b(y,x)$ - at any rate, the $x$ is being complex conjugated when you write it in terms of components. The vector $|j_1j_2 jm\rangle$ is a basis vector in the same tensor product space $H_1\otimes H_2$ which has eigenvalue of $(\vec J_1+\vec J_2)^2$ equal to $j(j+1)$ and the eigenvalue of $J_{1z}+J_{2z}$ equal to $m$. The Clebsch-Gordan coefficients are translating the two bases into one another.
May
24
comment state vector notation
Otherwise, $|jm\rangle$ is a state in the $(2j+1)$-dimensional representation of $SU(2)=Spin(3)$ whose eigenvalue of $J_z$ is equal to $m$. So the states $|jm\rangle$ for $m=-j,-j+1,\dots j$ form an irreducible representation of the $SU(2)$ group. For different values of $j$, we get different representations. $|j_1 m_1 j_2 m_2\rangle$ is just a basis vector in the tensor product linear space of two angular momenta, it's just $|j_1m_1\rangle\otimes |j_2m_2\rangle$.
May
24
comment state vector notation
Dear @okj, unless stated otherwise, an extra comma or semicolon separating the labels should make no difference. ;-) Otherwise, $|S_x,+\rangle$ surely can't be simplified to $|+\rangle$ because the normal component that the spin measurements refer to is $S_z$, not $S_x$, so the $S_x$ refinement is quite important to make it clear what state one is talking about. The $|S_z,+\rangle$ state is an eigenstate of $S_x$ which is a linear combination of both eigenstates of $S_z$.
May
24
comment Conservation law of energy and Big Bang?
Dear @Dan, you're not right about physics but you're also wrong about the history (independently of the fact that, as I agree, the history is totally irrelevant for the validity of the conservation law). Emmy Noether actually found her Noether's theorem in the very same year when Einstein completed his general relativity, 1915, see en.wikipedia.org/wiki/Emmy_Noether#Physics - so it was totally available to Einstein.
May
24
reviewed Approve The “Nerd Sniping” problem. Generalizations?
May
24
answered Conservation law of energy and Big Bang?
May
23
revised Home-made lattice calculation?
added 17 characters in body
May
23
answered Pressure inside a light bulb
May
23
answered Home-made lattice calculation?
May
23
comment Are black hole states completely mixed?
Your question isn't specific for black holes and it depends whether one considers a microcanonical or canonical ensemble. In general, a black hole with well-defined enough geometry also has a sharp enough temperature, so one may write $\rho$ as a thermal density matrix but there's still the freedom to consider the different ensembles. Their macroscopic consequences are identical in the large black hole limit - the thermodynamic limit.
May
23
answered Why is travelling around the speed of light a problem?
May
22
answered Why is it valid to take the partial trace to describe a subsystem?
May
22
revised Uniqueness of quasiclassical consistent histories
added 111 characters in body
May
22
answered Uniqueness of quasiclassical consistent histories
May
22
comment Quantum Physics and the Law of Large Numbers
Great to hear you saying so many sensible things, @Peter, although arguably a bit short. ;-)
May
22
comment Question about gravity probe B
Dear David, you have diluted what has happened and what has been shown in such a way that 1) one loses the idea why the experiment would be paid for in the first place, and 2) one isn't sure what you wanted to say. Were those the goals of your remarks? ;-) It's surely another confirmation of GR in the regime where we expected it to be correct, anyway, but with every test that is independent of the previous ones, at least partially, our confidence in GR increases.