For centuries people have watched the stars appear after dark. The dark sky is pierced with a few thousand pin points of light. On a clear moon less night one may see clouds of stars in the Milky Way. Sometimes, if it is very dark and clear, you might see tiny smudges from a handful of globular clusters and nearby galaxies. A telescope opens the eyes to millions of stars. The dark sky is essential for observing the stars. Deep thinkers such as Kepler, Halley and Cheseaux began to wander: why is it dark at night? The problem was popularized by the German astronomer Heinrich Wilhelm Olbers in an article "On the Transparency of Space" in 1823. Olbers wrote, "If there really are suns throughout the whole of infinite space, and if they are placed at equal distances from one another, or grouped into systems like that of the milky way, their number must be infinite and the whole vault of the heaven will appear as bright as the Sun. . . ." If the universe is extremely large, static (unchanging), and populated with uniformly distributed almost infinite number of stars, the entire night sky should be ablaze with light. Olber's Paradox simply asks, Why is the night sky dark?

Imagine walking through the woods. There may be a lot of clear space between trees, but the horizon is filled with trees. You will see nothing but trees, even if the trees grow together in clumps like bamboo.

Consider a number of imaginary thin spherical shells centered on the earth. Imagine for a moment that astronomical formulas and constants are the correct way to understand the universe.  In the formula, the variable r measures the radius of each shell in parsecs. The number of stars in each shell depends on the volume of the shell and the average density of stars per unit volume. Let the thickness of each shell be one parsec. The number of stars per shell should be N = 4 r² k ( since the thickness is always one). The average density of stars per parsec³ is k. The brightness of each star is F = L / r ², where L is some constant of luminosity for an average star. Notice that the brightness decreases with the square of the distance (r) and the number of stars increases with the square of the distance. The total light from each shell arriving on earth should be NF:

NF (total stars * average Luminosity) = 4 r² k L / r ²
The r² cancels. We are left with nothing but constants => NF = 4 k L

This means that each shell should have the same luminosity as every other shell independent of its distance. At the distance of hundreds of millions of parsecs, the sky should brighten until we are all roasted by the light from trillions of stars. Olbers' paradox asks, Why is it dark?

Some proposed solutions

1. Stars are not evenly distributed. Only a trillionth of the volume of our galaxy may be occupied by stars. At increasing distances, space is mostly empty with stars clustered in galaxies. At greater distances galaxies themselves bunch up in clusters and super clusters. The assumption about even distribution is certainly not accurate for a small number of shells. As the number of shells increases to millions of parsecs, the clumping of stars should not affect the luminosity. If Olbers' assumptions are correct, at the volume of space containing billions of galaxies, the night sky should be as bright as the surface of the sun.

2. Perhaps we don't see all the stars because the light is blocked by dust and gas. The dust should act like a black body and absorb the light. It should then transmit it at lower frequencies. Eventually the dust should glow like the distant stars and the sky should still be bright. Someone could argue that close by dust blocks the light bouncing off more distant dust. If there is that much dust, it should obscure even neighboring stars. Photon collisions with interstellar gas should make light scatter. The scattered light from distant galaxies should be out of focus like the sun at sunset. The idea that light from the stars is blocked does not seem to work.
 

3. The universe is older than the stars we see. The light from the farthest stars just hasn't had time to reach us yet. This is the light horizon solution. Some of the distant light is below our time horizon. Maybe future generations will burn up when the distant light "dawns."

4. The universe is expanding. An expanding universe does not imply objects are flying through static space. Space time is being stretched out. This explanation says the light has dimmed and reddened because of the expansion of space time. It is interesting that the "deep field" HST photo shows a large number of very faint objects which are blue in color. Shouldn't these extremely distant objects appear red after having been sifted in the red direction by space time expansion? 

5. The "Big Bang" uses both #3 and #4 above. According to this scenario, the light from the creation of atoms has moved from a black body temperature of 3,000 K to 2.73 K due to the expansion of space time. The redshift affects the brightness as well as the color. The accepted modern solution to Olbers' Paradox is that the big bang creates a light horizon and the expansion of space time lowers the light intensity and shifts it into the invisible red spectrum.

A star does not radiate with equal intensities at all frequencies.  The 2.73 K Cosmic Background Radiation has an intensity peak with a wavelength of about 1.1 millimeters (0.0011 meters.)  Scientist claim that when the universe cooled to 3000 K, neutral atoms began to form.  At this point matter and radiation decoupled, and the universe became transparent to light.  They claim that the cloud of photons seen in the Cosmic Background Radiation originated some 100,000 years or so after the Big Bang.  The black body peak for 3,000 K lies in infra red at a wavelength of 960 nm (0.000000960 meters.) The wavelength of the Cosmic Background is about 1100 times as long as its original wavelength. The universe (space time) has expanded and is now 1100 times larger than when neutral atoms first formed.  It is known that a light source moving relative to the observer is shifted in frequency due to the Doppler effect.  Many scientists also believe the universe's expansion increases the wave length of light in proportion to the change in space time.  This stretching out of space time has shifted the black body peak from 3000 K to 3 degrees above absolute zero. The adherents of this model say that the Cosmic Background Radiation is evidence for the expansion and the big bang.

Evidence from the universe is different from laboratory experiments. In a lab, an experiment can be modified to test the hypothesis. In the universe, all theories rely on assumptions about the nature of space, time and matter. These assumptions are difficult to test without circular reasoning and circular experiments. For example, ideas about gravity depend on ideas about mass. Mass is measured by its effect on acceleration. The definitions for accelerations depend on the concept of mass.   Ideas about gravity can accurately place spacecraft into orbit around distant planets. That does not mean the ideas are true, since gravity inevitably is used to explain gravity.  If there were "real change" such as the archaic peoples believed in, you could not detect it using the ideas of mass, acceleration, and force.  Astronomers test the spectrum of gases in the lab. They rely on untested assumptions, however, when these spectra are used to explain the distant universe.

If the Big Bang were false, would it be dark at night?

This web page is dedicated to thinking about the most basic assumptions. The Greek philosophers invented the modern way of thinking. Their ideas about astronomy were mostly false. How could they have been wrong so often and yet have established the foundations for Western science?  The most important question they struggled with was change. If the universe was primarily a place of change, how could a philosopher figure out anything? Everywhere you look there are motion and change. Plants grow, die, and revert back to compost. Metals tarnish or rust away. People are born, inquire about their surroundings, and then die. Food changes to bone and muscle. Mountains spring up from the earth and then erode away. The sea pounds great rocks into beaches of sand. Ancient ruins are sometimes dug out of the earth. The stories from the earliest people tell of planet gods who fought catastrophic battles in the skies. The ancient traditions told of those who lived before the bronze age during a "timeless" age. These traditions from the past implied that change affected everything.

In the face of all this change, how could a philosopher find wisdom? They struggled with this problem for generations. Some philosophers proposed that all change was a figment of our imaginations. Others imagined invisible atoms that were changeless. Plato adopted a world of ideas where "forms" did not change. Then Aristotle came up with a brilliant idea. All modern people adhere to Aristotle's idea. It is the fundamental idea. The idea is never questioned or tested by modern peoples. Read Aristotle and ask yourself the question, "What idea did he have that defined the entire cosmos both near and far?" Modern scientists are schooled in Aristotle's assumption, although most have never heard of it. It is the unstated idea that is behind their whole way of thinking. It is unlikely that a scientist could ever think of the universe apart from Aristotle's fundamental idea.

Aristotle tells us that the most important or elementary ideas must be assumed. They cannot be proved. All systems of knowledge are built on faith. This faith is blind, because it accepts these foundational ideas without question. Scientists have the most amazing faith. They believe the whole universe works according to the idea that Aristotle invented. What if Aristotle's idea is false. That would be a serious problem for Western intellectuals. If you remove their foundation, what can they stand on? They have no idea how to think about physical things apart from the assumption.

The archaic peoples thought about the universe and change opposite from the philosophers. The Sumerians had records of the past that shows their universe really changed. They also believed in planet gods. Their histories were stories about the planets and how they changed the earth and each other. Is it possible to reject the fundamental assumption and not buy the idea that all change is caused by the gods? The writers of the Bible did just that. They did not have a Western view of the physical realm. Their world view was similar to the pagans but minus the planet gods.

Modern Christians accept Aristotle's idea. It is entrenched in Western thinking. They interpret Bible history according to this assumption. Many of the earliest scientists, like Newton, were Christians and saw science as the natural extension of the Bible. They interpreted the Biblical record of the past by means of the Greek assumptions. The Bible warns about the stoicheon (elemental ideas) of the philosophers. Despite this warning, Newton imagined a static universe with absolutely unchanging time and space. Einstein revolutionized science by making space and time relative. Einstein, educated in the Greek way of thinking, found a way to imagine a dynamic universe while still adhering to the fundamental assumption. What if Einstein were wrong? Don't experiments assure us that he is right? Every experiment that tests Einstein's ideas is based on Aristotle's assumption. There is contrary evidence in the records of the ancient astronomers.

The best way to think of the universe is to get rid of this assumption. That is not easy to do because you have to throw out your whole system of reference. It also does not make the universe less complex. It just lets you see the simple nonscientific answer to its complexities. The universe is full of paradoxes and mysteries. Why does the universe act like it is full of dark matter? Why is ancient starlight shifted into the red? Why is it dark at night? Solving the darkness problem does not require mathematics. It only requires you to break free of the fundamental assumption. You will be left with a "really dynamic" universe. You will see that Olbers' assumptions are suspect. You may glimpse the simple answer to the dark sky paradox.

Copyright 2000 Victor McAllister
All Rights Reserved.
Latest revision February 5. 2004 

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