Recent content by emma83

Homework Statement Shannon entropy is a concave function defined as follows: H(X)=-\sum_{x}p(x)\log p(x) Conditional Shannon entropy is defined as follows: H(X|Y)=\sum_{y} p(y) H(X|Y=y)=-\sum_{y} p(y)\sum_{x}p(x|Y=y)\log p(x|Y=y) Can we deduce that: \sum_{y} p(y)H(X|Y=y)\geq H(X|Y=y)Homework...

Well I need the symbolic expression for the rest of the assignment. Do you think this is not solvable?

Thanks for your answer. I had to translate it from French, it is not in a textbook but part of an assignment I have to do for a physics course. Actually I am allowed to use a computer program to get the answer, so it should be enough if Maple, Mathematica or Matlab gives me the symbolic...

Homework Statement Find the inverse function f^{-1} of the binary entropy f (given below) on the domain of definition [0;1/2[ (i.e. where f is continuous strictly increasing). The function f is given by: f(x)=-x\log(x)-(1-x)\log(1-x) (where \log is the logarithm base 2) Homework...

Hello, What is the difference between an unstable and an unbound orbit of a particle around a black hole? As far as I understand, an unbound orbit is (informally) a trajectory which does not represent a closed curve (such as an ellipse) around the black hole, and this condition formally...

Dear George, Thanks a lot for your answer. First, yes sorry I misplaced the indices in the first relation, the correct relation is: k'_{a}=(\delta_a^{b} + \lambda_a^{b} d\tau)k_b Concerning d\tau, it is actually a \delta u, where u is the affine parameter along the trajectory of a photon...

Well I had of course already checked beforehand the wikipedia page on Pauli matrices (http://en.wikipedia.org/wiki/Pauli_matrices) but had not found a relation to solve this problem... So Ryuunoseika, which article are you talking about ?

Hello, I am trying to recover the following calculation (where K,A are 4x4 matrices in SL(2,C)): --(start)-- "We expand K'=AKA^{\dagger} in terms of k^a and k'^{a}=(\delta_a^{b} + \lambda_a^{b} d\tau)k^b. Multiplying by a general Pauli matrix and using the relation...

What is the difference between a free-falling frame and a Fermi-Walker frame ?

Thanks, actually I found an answer for A_{k} without the details of the calculation. I tried to compute A_{k}k_{0}A_{k}^{\dagger} but I don't get k as would be expected. The proposed solution is: A_k=\frac{1}{\sqrt{2C(1+n_3)}} \left( \begin{array}{cc} C(1+n_3) & -n_- \\ Cn_+ & 1+n_3...

Well, thanks Fredrik but now I really would like to know how to do "the rest" !

Hello, Is the law for matrix multiplication in SL(2,C) the same as usual ? I try to solve the equation A_{k}k_{0}A_{k}^{\dagger}=k where k_0 corresponds to the unit vector \{0,0,1\} and k is an arbitrary vector, i.e.: k0= \left( \begin{array}{cc} 2 & 0 \\ 0 & 0 \\ \end{array} \right)...

Hello, If I understand well, since a Lorentz transformation applied on a particle induces a Wigner rotation which depends on the momentum, the spin reduced density matrix that is naively done by tracing out the momentum has no (Lorentz) transformation law. Only the overall system can be...

Can somebody explain me what are precisely the polarization vectors of a photon and how they relate to the photon's momentum and helicity ? Or give me reference of textbooks in which I could learn more on this topic ? Thanks a lot for your help!

Thanks, this is indeed what I am looking for. Do you know maybe if it is possible with the Kerr metric (given, e.g. the metric in the Boyer-Lindquist coordinates) ?