In our current best model, the Universe is infinite and ever expanding. In this model, it is thought that every line of sight eventually ends at the photosphere (outermost visible layer) of a star. If so, it may be argued that the night sky should be brilliant - as bright as a typical star. The fact that the night is dark is known as Olbers' Paradox.
Here are some explanations:
1) Light dilutes in strength as distance^2.
2) The dust between the stars blocks the light.
3) The expanding Universe "reddens" the starlight to longer wavelengths, since space expands as the light waves pass through it.
Why are all of these wrong or incomplete? E.g., for number 3, why then is the night sky not brilliant at long wavelengths?
What is the most complete explanation, and what poet found the answer?
1. The premise that "every line of sight eventually ends at the photosphere (outermost visible layer) of a star" is based on the assumption that stars are uniformly distributed in space. If that is the case, then the number of stars per square degree, or per steradian, of sky increases as the square of distance, balancing out the decrease per star.
The initial counter to this was that stars are not distributed uniformly, but rather stars are in star clusters, which themselves are separated into galaxies, beyond which there's emptier space until you get to other galaxies, which also cluster into galactic clusters, and then into superclusters, etc.
This is a better solution than the inverse square law. If the average star in our galaxy is say 25,000 light years away and is of the order of one million miles in diameter, it subtends about 7x10^-18 radians or 4x10^-16 degrees and has an angular area of around 1.5x10^-31 square degrees. As there are about 41253 square degrees in the full sphere of the sky, this is about 1/(3*10^35) of the sky.
If a line of sight therefore has only such a small chance of hitting another star within our galaxy, if we assume that its chance of hitting another galaxy is similarly as small, and of hitting a star withing that galaxy, and that this hierarchy continues ad infinitum, the probability of hitting any star at all can be found by an infinite series, where a and r are both 1/(3*10^35): a + ar + ar^2 + ..., which is tiny.
Minor differences in r from one level of the hierarchy to the next would vary this from the strict geometric series, but the idea would be the same. However, recent discoveries show that galactic clusters do not arrange themselves in higher orders of cluster, but rather form walls of galactic clusters, spread in intergalactic space like the walls between cells of a kitchen sponge, so even this doesn't provide an ultimate rescue.
2. The dust itself would be absorbing all that energy and would become glowing hot, thereby not resolving the paradox.
3. This gets closer to the truth. In fact, in the early universe there was cosmic expansion, as mentioned in Daniel's post, separating (from us) all but our observable universe, which is therefore finite.
I would disagree with Daniel's atmospheric barrier as that suffers from the same problem as the galactic dust.
I've heard that the "modern" solution is that there's just not enough energy to go around to allow the sky to be as bright as the solar disk. But that leaves open the question of why there is not that much energy. I'd say the hierarchical nature answers to a point, but ultimately it is the differentiation of the observable universe from the possibly infinite full universe that answers the question of why not every sight line terminates in a stellar surface or its co-question of why there's a finite amount of energy.
I'm sure the sky, even at night, would be a lot brighter if the observable universe were just as crowded with stars as an individual galaxy is (assuming hypothetically it wouldn't collapse on itself from gravity).
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Posted by Charlie
on 2018-07-24 10:14:27 |
my version
