I'm trying to find out more about an alternate solution to Olber's Paradox (the sky shouldn't be dark in an infinite eternal universe) : the structure is a fractal. Yes yes, the real Universe isn't a fractal, but it's a neat idea and fun to try and visualise.
Apparently some dude named Fournier found a fractal structure (sometimes it's called a "proto-fractal", not sure why) back in 1907 which allows large blank areas of sky, even though it's infinite in size. Couldn't find out much more than that but I did stumble upon an image of it, so it was easy to make a looping zoom animation.
I can't find much more in the way of fractals that would look more like the real sky that would also allow blank lines of sight. "Fractal cosmology" searches tend to turn up raving loonies or advanced mathematics I don't understand. Hmmm.
Fractals don't really solve Olber's paradox, though, at least not for an infinite series. This allows for regions of infinite luminosity and regions of zero luminosity, but still doesn't give us a black sky.
ReplyDeleteI'd love to see a 3d simulation of this, though. I wonder what that sky would look like exactly.
The CMB isn't thermalized starlight. It's light that predates the stars, redshifted to sub-millimetre wavelengths.
ReplyDeleteI'm not sure that we would be "blinded" by the CMB if we could see it. Surface brightness doesn't vary with distance (unless space is expanding). So if it was simply redshifted starlight (presumably by some other mechanism than expansion, a la tired light), shouldn't the sky still look infinitely bright ? Infinite number of stars = infinite energy, whatever waveband it's in.
ReplyDeleteEDIT : In my early-morning delirium I forgot about redshift dimming, the Tolman test etc. Will edit later, unless Christopher Cooke gets there first. :)
Christopher Cooke
ReplyDelete"Fractals don't really solve Olber's paradox, though, at least not for an infinite series. This allows for regions of infinite luminosity and regions of zero luminosity"
This one is giving me a headache. :P
I believe the idea is that at increasing distances the density of stars decreases, so that even if you integrate to infinity you don't necessarily get infinite energy. I guess the analogy would be the integral under a Gaussian, which is finite if integrated over infinity, or some other convergent function. But this is me trying to wrestle with ideas I don't understand using maths I don't remember how to do before breakfast. :)
Though I have difficulty understanding how this solution can work for discrete stars rather than a continuous emission of radiation. Finite energy from stars of equal energy output requires a finite number of stars. And if you have a finite number of stars along an infinite line, it follows that there must be a most distant star*. Which means a) fractals aren't necessary and b) there's an edge beyond which there are no more stars, and given enough time the whole thing will collapse into a big ugly heap.
ReplyDelete* EDIT : Unless they're all infinitely far away from one another. Which they aren't.
If, on the other hand, you have an infinite number of stars along an infinite line of sight then there'll still be infinite energy along some lines of sight, so you have the problems of the original paradox again.
http://www.astro.ucla.edu/~wright/stars_vs_cmb.html
ReplyDeleteHenry K.O. Norman Everything in astrophysics is an interpretation. It just happens that my explanation is the accepted interpretation of the observations, and the interpretation that you asserted (without making mention that it, too, was an interpretation, I might add) isn't only fringe, it doesn't match the observations.
ReplyDeleteChristopher Cooke To be fair, he did call them both interpretations in his second post, just not in the first. Though I'd say the link I posted does a good job of explaining why that particular interpretation is not compatible with observational data.
ReplyDelete