Wednesday, June 28, 2017

120 - gasp! gasp!

the gravitational entropy $S$ in a FLRW-universe can be estimated to be proportional to the ratio between the Hubble-length and the Planck-length, all squared. can you write down an expression for $S$ only in terms of the constants of Nature?

Wednesday, June 21, 2017

120 - gasp!

compute the number of bits that can be stored by a sphere with the Hubble-radius $\chi_H$ and compare that number to the factor by which a naive estimate of the dark energy density is larger than the actual density $\rho_\mathrm{crit}$... surprised?

Wednesday, June 14, 2017

magic of Pauli-matrices

in the last two weeks CQW asked about the generation of rotations and Lorentz-transforms from the off-diagonal Pauli-matrices $\sigma^{(1)}$ and $\sigma^{(2)}$. what type of transformation would be generated by $\sigma^{(0)}$ and $\sigma^{(3)}$? what types of transformations would be commutative?

Wednesday, June 7, 2017

Pauli and Euclid

can you show that rotations $R_{\mu\nu}$ are generated by the Pauli-matrix $\sigma^{(2)}_{\mu\nu}$ with the angle $i\omega$ as an additive parameter?