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--------------------- 2630 - OLBERS PARADOX - why is the sky dark?
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- In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, then any line of sight from Earth must end at the very bright surface of a star and hence the night sky should be completely illuminated and very bright. Our nights should be filled with starlight?
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- If the Universe is truly infinite and there are really an infinite number of stars out there, then in every direction we look in the night sky we should see a star. We don’t. There is a lot of darkness out there.
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- If we were in the middle of an infinite forest on flat land, the forest would have an infinite number of trees and whatever direction you look your line of sight would eventually run into a tree. The same thing should happen in the night sky. No matter which direction you look in an infinite Universe you would eventually see star light. The night sky should be glowing in starlight, not darkness. What’s up?
- The darkness of the night sky is therefore evidence for a dynamic universe, such as the Big Bang model. That model explains spacetime's expansion, which lengthens the light originating from the Big Bang to microwave levels via a process known as redshift. Visible light wavelengths get stretched in expanding space making the light lose energy and broaden the wavelength into the microwave frequencies.
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- This microwave radiation background has wavelengths much longer than those of visible light, so the light energy appears dark to our naked eyes. Expanding space stretches light wavelengths from their original optical to broader microwave wavelengths outside our eyes ability to see them.
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- One way to see the early astronomer’s point of view is to divide the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell, which is between 2,000,000,000 and 2,000,000,001 light years away
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- . However, the second shell is twice as far away, so each star in it would appear one quarter as bright as the stars in the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell.
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- Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is. That is, the light of each shell adds to the total amount. Thus the more shells, the more light; and with infinitely many shells, there would be a bright night sky. Something ain’t right with this logic?
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- Johan Kepler saw this as an argument for a finite observable universe, or at least for a finite number of stars.
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- In Einstein’s general relativity theory, it is still possible for the paradox to hold in a finite universe, though the sky would not be infinitely bright, every point in the sky would still be like the surface of a star.
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- The Big Bang theory involves the expansion of space, which can cause the energy of emitted light to be reduced via “redshift. The extremely energetic radiation from the Big Bang has been redshifted to microwave wavelengths (1100 times the length of its original wavelength) as a result of the cosmic expansion, and thus forms the cosmic microwave background radiation.
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- This explains the relatively low light densities and energy levels present in most of our sky today despite the assumed bright nature of the Big Bang. The redshift also affects light from distant stars and quasars, but this dimming is minor, since the most distant galaxies and quasars have redshifts of only around 5 to 8.6.
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- ok, astronomers decide they have to do the math:
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- Astronomers have found that galaxies on the largest scale fill all of space more or less uniformly and have measured the density of the galaxies in the Observable Universe to be 0.0029 galaxies per cubic million lightyears. Astronomers estimate that there are 10^10 stars in the average galaxy. So, on average there must be 2.9*10^7 stars per cubic million lightyears.
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- So the next question is that if we know that density of stars and we know the average cross-section of the average star we can calculate the distance that your line of sight can travel before running into a star. (MLY = million lightyears).
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- The average star is 7*10^8 meters in diameter, that is 3.5 *10^8 meters radius.
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- The cross-section area is pi*r^2 = 38*10^16 meters^2.
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- The density is 2.9*10^7 stars/MLY^3
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- The density (with a lightyear = 9.5*10^21 meters) is = 0.34*10^-58 stars / meter^3
- The concept here is that a line of sight traverses a distance (dx) until it hit’s a star. If we know the density of stars per unit volume, (n), then the number of hits per unit area lying in the line of sight is (n) * (dx) = (number of stars per cubic meter) * (distance to hit a star).
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- If each star has a cross-section area of (A), then the number of collisions with stars = “N” = (A)*(n)*(dx). If we set the number “N” equal to “1” then calculate the distance we travel before we hit the first star, 1 = (A)*(n)*(dx).
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--------- 1 = (38*10^16 meters^2) * 0.34*10^-58 stars / meter^3 * (dx)
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---------- dx = 7.6*10^40 meters
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---------- dx = 8*10^24 lightyears
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---------- dx = 8*10^18 million lightyears.
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- So the average distance your line of sight would travel before landing on a star is 8*10^15 billion lightyears. However, the Universe is only 13.7 billion years old. So, the sky is dark because our line of sight has not landed on a star yet in most every direction we look.
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- This also means that Cosmic Inflation is one explanation for the Universe expanding faster than the speed of light in its early formation. That is the only way that stars could get that far away. The edge of the Observable Universe is 10^10 lightyears away and the distance to that first star in any line of sight is 10^24 lightyears. Therefore the Observable Universe is mostly Dark because the starlight has not reached us yet.
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- The Universe is not old enough yet, and, that light has not have “time” to reach us. Therefore, we have concluded that the night sky is dark because the Universe is finite, not infinite, and it has a finite age, not infinite.
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- Now, that we have the radius of the Observable Universe at 10^10 lightyears we can calculate the number of stars, since the density is 2.9*10^7 stars / million lightyears^3.
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- The volume of the Universe with a radius of 13.7*10^3 million lightyears. Multiply these two terms gives us 4.7*10^19 stars. Another estimate Astronomers come up with is that there are 10^11 galaxies and 10^11 stars per galaxy giving us 10^22 stars in the Observable Universe. This is within 2 orders of magnitude to our other calculation. So roughly, there are 1,000,000,000,000,000,000,000 stars out there.
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- How many stars would it take to have the same luminosity at night that we have in the day from our Sun? The luminosity of the Sun has been calculated to be 3.8^10^26 watts. Dividing by the surface area of a sphere that is 93 million miles in radius will tell us how much of this luminosity reaches Earth / meter^2. (F = flux f light).
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--------- F = Luminosity / 4*pi*d^2
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--------- F = 3.8*10^26 / 6.28 * (1.5*10^11 meters)^2
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---------- F = 1,300 watts / meter^2, very bright
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- How many stars like our Sun would we need out to 10 billion lightyears away in order to have the same brightness as daylight?
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--------- F = Luminosity / 4*pi*d^2
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--------- F = 3.8*10^26 / 6.28 * (10^11*9.5*10^15 meters)^2
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---------- F = .68*10^-26 watts / meter^2, very dim
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- How many stars would have to be out there to have the same brightness as daylight?
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--------- N = 1.3*10^3 watts / m^2 / .68*10^-26 watts / m^2
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--------- N = 2*10^29 stars
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- We would need 10^31 stars to have daylight and we only have 10^22 stars. That is a 10 million times more stars are needed to light up the night sky to daylight.
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- But, how about lighting up the night sky just to starlight, instead of sunlight. How many stars would that take? A typical star might be Proxima Centauri that is our second closest star at 4.2 lightyears away. The luminosity is 0.0006 Solar Luminosity. Using the same formula as above the flux we see is 22.8*10^-22 watts / m^2.
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- How many stars would have to be out there to have the same brightness as starlight?
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--------- N = 22.*10^-12 watts / m^2 / .68*10^-26 watts / m^2
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--------- N = 3.2*10^14 stars
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- We would need 10^17 stars to have solid starlight in the night sky, and we have 10^22 stars out there. There are enough stars out there, there must be more to explaining why the night sky is dark.
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- The rest of the answer lies with the fact that the Universe is not static. Unlike the trees in the infinite forest the Universe is expanding. At the edge of the Observable Universe the Universe is expanding faster than the speed of light and that light will never, never reach us.
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- The Cosmic Microwave Background radiation solves this in an amazing way. Each line of sight does indeed reach a star. There are enough stars out there to light the entire night sky with the brightness of a starlight.
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- But, we are like inside this oven, and the temperature is so small because the expansion of the Universe dilutes the radiation emitted down to harmless microwave energies, at temperatures of only 2.725 degrees above Absolute Zero. The wavelengths of starlight have been redshifted to these much longer microwave wavelengths.
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- There are other explanations for darkness that do not hold water. One is that the dust in intergalactic space blocks the starlight. Well, this only works for a little while because the radiation would eventually heat up the dust to the same temperatures and it would begin radiating on its own. We would still see light in every direction even if much of it would be infrared light coming from the dust.
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- Another explanation is that the stars are dying. They do not have an infinite lifetime and many of these 10^22 stars would have evolved into Neutron Stars or White Dwarf stars that no longer radiate much light. These stars would be dark in the night sky.
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- This does not work either because past every dark star must lie another lighted star. And, new stars are being born out of the dead stars that go dark. New light is constantly being produced. Dead stars are not the reason for the dark sky.
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- The Universe is believed to be 10^58 meters in radius, or 10^42 lightyears. The Observable Universe is 1.37*10^10 years old and 10^26 meters in radius. The night sky is dark because we can not see most of the Universe, what we see is finite and much of the light has not reached us yet because the Universe is a finite age and there has not been enough time.
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- Lastly, the night sky is dark because the Universe is expanding and the light radiation has shifted into darkness to our eyes, into the microwave region.
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- In the Dark of Night, astronomers are making these calculations. The math was there astronomers just had to discover it. But, it seems like such a simple question.
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- Why is the night sky dark? Why is the day sky blue? Little kid questions. Better do well in school if you are going to discover the answers. The Universe is more complicated than you can imagine.
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- February 23, 2020 865 2630
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--------------------- Monday, February 24, 2020 --------------------
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