Wednesday, January 18, 2017

very heavy and very light

can you explain why the ratio between the Hubble mass (i.e. the mass inside the Hubble volume today for a critical universe) and the Planck mass is about $10^{60}$? why are stars roughly in the middle (on a logarithmic scale)? or even more puzzling: why's the ratio between Hubble and Planck-mass about equal to the ratio between stellar masses and the masses of nucleons?

Wednesday, January 11, 2017

forces on dust particles

can you compute the ratio between radiation pressure and gravity acting on a dust particle in the solar system? could one relate the two forces to the mass of the Sun and establish a minimal mass from which on there would be no dust and hence no planetary system?

we wish all CQW-readers a successful year 2017 full of cosmological discoveries.

Wednesday, January 4, 2017

funny way of writing Maxwell's equations

can you reformulate the Maxwell-equations in terms of the complex-valued field $\vec{X} = \vec{E}+\mathrm{i}\vec{B}$? would there be potentials $\Phi$ and $\vec{A}$ for $\vec{X}$, and can one even find a covariant formulation?

Wednesday, December 21, 2016

comets and their tails

why is the tail of a comet curved? and could you estimate how fast the curvature of the tail could change?

with this very christmassy question we wish all followers of CQW a merry x-mas and a happy and successful year 2017. we hope to see you again in january.

Wednesday, December 14, 2016

Poynting-flux and magnetic charges

in the derivation of the Poynting-theorem one needs to substitute a term $\vec{B}\mathrm{div}\vec{B}$, which is equal to zero due to the fact that the magnetic field is purely rotational, $\mathrm{div}\vec{B} = 0$. insisting to introduce magnetic charges by requiring $\mathrm{div}\vec{B} = 4\pi\rho_\mathrm{mag}$, would that lead to a violation of energy-momentum conservation? are there other arguments, e.g. from the covariance of electrodynamics, why this is not possible?

Wednesday, December 7, 2016

electrodynamics with non-conserved charges

following up on last week's question: could one construct a theory of electrodynamics with non-conserved charges, i.e. where $\partial^\mu\jmath_\mu\neq 0$? what consequences would that have?

Wednesday, November 30, 2016

gravitational fields for non-conservative systems

Einstein's field equation links the Einstein-tensor $G_{\mu\nu}$ to the energy-momentum tensor $T_{\mu\nu}$, which is divergence-free, $\nabla^\mu T_{\mu\nu}=0$. energy-momentum conservation is usually established by considering fields whose Lagrange-density $\mathcal{L}$ does not have an explicit dependence on time or position, leading to the definition of $T_{\mu\nu}$ with the corresponding continuity. in what way would fields $\phi$ with $\mathcal{L}(\phi,\nabla^\mu\phi,x^\mu)$ source a gravitational field?