Space Forum / Space Science / January 2008

-> There's something I find strange about Olber's paradox.
-> Let me lay out a 3D XYZ cartesian grid, with arbitrary
-> units of 1 mile, and at each vertex let there be a person.

-> Now I'll send out a light signal from the origin spreading
-> to all persons, at which time they each begin humming a
-> tune, generating a faint sound. (We'll assume sound
-> is carried by the medium).

-> Now according to Olber, the amplitude of the humming
-> will build indefinitely, in fact to infinity.
-> See the problem, the sound energy generated is every
-> where of finite density, i.e. 1 hummer/cubic mile, yet
-> the sound becomes infinitely dense.
-> Is there something wrong with that?
-> Regards
-> Ken S. Tucker
 
The sound isn't of finite density; the hummers are. Each hummer is
feeding sound energy continuously into the medium, and we are assuming
that the sound never degrades, gets absorbed, etc.. So the intensity of
sound builds up and up, with no limit within the parameters of this
fantasy.
 
If the hummers consist of a sound-absorbing material, then the level
of sound will reach a limit when the rate at which each hummer absorbs
sound equals the rate at which he produces it. This is analogous to the
astronomical Olber's paradox, which does not say that the intensity of
light would be infinite, but that it would equal the mean brightness of
a stellar surface. At that point, each star would absorb as much light
as it produces.
 
                                   dow