Thursday, April 26, 2012

fine structure constant

what would be different in cosmology if the fine structure constant would not be 1/137 but 1/138?

bonus points: why do we know that it has has stayed constant in the course of cosmic history?

Thursday, April 19, 2012

Olbers' paradoxon

classic cosmology question: why is it dark at night? what are minimal assumptions for answering this, and how would you reply with the knowledge of a FLRW-cosmology? are there other (astrophysical) explanations you can think of? could you construct an alternative whacky cosmology (i.e. non-FLRW) that would resolve the paradoxon?

bonus question: what's $(\pi+20)^i$ with $i=\sqrt{-1}$? surprised?

Thursday, April 12, 2012

to infinity and beyond...

suppose you've got a spaceship with amazing engines that are able to provide an acceleration of $1g$ measured inside the rocket, such that you would not notice any difference to living on Earth.

what's the time measured on clocks inside the rocket that would pass while travelling
1. to the centre of the Milky Way?
2. to the most distant quasars we see today?
3. the Hubble distance?

Wednesday, April 11, 2012

CMB dipole - fact or fiction?

the cosmic microwave background has a dipolar structure which is interpreted in terms of the Milky Way moving relative to the CMB, inducing Doppler-shifts in the photon energies and boosing the flux. would it be possible to distinguish between a motion dipole and a cosmological dipole on the last-scattering surface? why is the Doppler-boosted photon spectrum still a Planck-spectrum with the correct Wien- and Stefan-Boltzmann-laws?

bonus question: what's $\int\mathrm{d}x\:x\ln(x)$?

Thursday, April 5, 2012

digits in physical constants

have a look at a table of physical constants, which are numbers spanning a wide range, and count the occurrence of the digit "1", of the digit "2" and so on. you will find, that the digit "1" occurs more often than "2", with decreasing frequency down to "9". is that odd?