5 THE EXPANSION OF THE UNIVERSE

Olbers started with a uniform distribution of stars in an infinite large space (number of stars per ly^3 - cubic lightyear - is constant) and the Sun is one of them. Consider a spherical shell around the Sun of 1 ly thickness and radius of R ly. The volume of the shell, and thus the number of stars in it, varies with R^2. When R is 3 times as big, then there are 9 times more stars in the shell. (Two dimension, length and width, vary while the 3rd dimension, its thickness, is fixed at 1 ly. Therefore the volume of the shell varies with R^2 and not with R^3). The brightness of a star in the shell decreases with R^2. When R is 3 times larger the luminosity of a star in the shell is 9 times smaller. So the increase due to the number of stars in a shell is just canceled by the decrease of luminosity per star. As a result on the average the luminosity of the shell as a whole doesn't change. A shell around the Sun of 1 ly thickness at 100 ly distance is as bright as a shell of 1 ly thickness at 1 billion ly around the Sun. Now realize the space of Olbers is build from an infinite of this kind of shells around the Sun, one neatly on top of the other. The sky at night should be infinite bright.

A Thought Experiment

Mind this solution does not depend on the size of the universe, nor on its age. It does not depend on whether the universe is expanding or not; the solution works also for the Steady State cosmological model. That is, the considered areas must be large enough for the cosmological principle to become apparent. And the age must be sufficient long for light to have crossed that areas, allowing the photon bath in a single area to become uniform. But it is not important whether the size or age is finite or infinite. It only depends on the density of the universe.

Of course expansion of the universe dilutes the radiation bath and lowers its average brightness. In the course of time from the Big Bang up to now the universe passes all densities from, well let's start at 10^17 kg/m^3 (neutron star density) down to 10^-26 kg/m^3 (critical density of the universe, that it is now, nearly). It depends on the precise moment in this elapse of time where you perform this thought experiment, what precisely is the value of the upper limit of the brightness of the sky at night.

Nowadays most molecular clouds have not yet contracted to stars, and not all star matter will finally convert to radiation. So, what is the actual radiation bath right now? The density of the universe as it is now consists of 73% Dark Energy, 23 % Dark Matter (WIMPs, neutrinos), 4 % ordinary matter (protons, neutrons, electrons) and only 0.005 % consists of photons (starlight and Background Radiation).

References
http://www.astronomy.ohio-state.edu/~ryden/ast143/Nov_18.pdf

NEXT PAGE                 Up                                 CONTACT

It's not dark! It's obvious!

THE SEA OF POSSIBILITIES: THE COLLAPSE OF THE WAVEFUNCTION  1  2  3  4  5
THE SEA OF POSSIBILITIES: EXPERIMENTS ON THE COLLAPSE OF THE WAVEFUNCTION  1  2  3  4
THE SEA OF POSSIBILITIES: FORWARD BACKWARD TIME DIRECTION  1  2  3  4  5  6  7
THE SEA OF POSSIBILITIES: THE DIRECTION OF TIME  1  2  3  4  5  6  7  8  9  10  11  12  13  14
NET FORCE IN REAL MATTER  1  2  3  4
NET FORCE IN QED  1  2  3  4  5
NET FORCE  1  2  3  4  5
QUANTUM QUATERNION DYNAMICS  1  2  3  4  5  6  7  8  9  10
NET FORCES IN QCD  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16
THOUGHT EXPERIMENTS ON MASSES  1  2  3  4  5  6  7
NEWTON EINSTEIN KIEKENS GRAVITATION  1  2  3  4  5  6  7
QUATERNION GRAVITATION  1  2  3  4  5  6  7
EXPANSION OF THE UNIVERSE  1  2  3  4  5
SPECIAL RELATIVITY  1  2  3  4  5  6  7  8  9  10  11  12
DIMENSIONS  1  2  3  4  5  6  7
TIMETRAVEL  1  2  3  4  5  6  7
EXISTENCE  1  2  3  4  5  6  7
CROPCIRCLES BY ELECTRIC AND MAGNETIC FIELDS  1  2  3  4  5  6  7  8  9  10  11  12  13  14
ADDITIONS  1  2  3  4  5  6  7
MATH  1  2  3
EVOLUTION  1  2  3
OTHER REMARKS ON BIOLOGY  1  2  3