Tikalon Blog by Dev Gualtieri

Olbers' Paradox

February 19, 2015

Elementary school science textbooks present the conduct of science in the simplified fashion of the "scientific method." According to this model, I see something unexpected happening in my laboratory, I frame an hypothesis of what might be happening, I make predictions based on this hypothesis, and my colleagues and I design experiments to see whether the predictions are correct.

As prediction after prediction is proven, there's a point at which my hypothesis becomes a theory; and, perhaps, centuries later, a law of nature. The process is somewhat different in fields of study, such as astronomy, where experiment is not possible. In that case, you just pile up evidence until everyone believes your hypothesis.

One important part of hypothesis formation is the power of analogy.[1] As George Pólya wrote in his short, 1945 book, How to Solve It,

"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

One example of the use of analogy in science is how the orbits of the planets around the Sun inspired the Bohr atomic model of electrons orbiting the nucleus. In that case, the 1/r² force of electrostatic attraction substituted for the similar gravitational attraction. This was a revision of a prior "plum pudding" analogy of electrons proposed by the discoverer of the electron, J. J. Thomson.

In electrical engineering, we have the hydraulic analogy of electrical current, voltage, and charge in a circuit. Electric charge is associated with the quantity of hydraulic fluid (typically, water), while current is associated with flow rate, and voltage with the pressure difference between two points.

One goal of science is the development of models for various "forests" based on observations of just their "trees." This idea of theory formation was succinctly stated by Richard Feynman when he made an analogy between how theories are developed and a study of the properties of chess by observation of chess pieces on chessboards.[2]

For example, observing a bishop long enough allows us to deduce that a bishop keeps its square color. Longer observation shows that this is the simple consequence of bishops being constrained to move on diagonals. Continued observation allows development of the more fundamental diagonal theory from the previous color theory.

There's one case in which an actual forest was used as an analogy in astronomy. When you're in a small stand of trees, it's possible to peer through the empty spaces to see what's outside. As the number of trees gets larger, the additional trees block your view of the outside world, and there's a point at which you can't see the outside world at all.

If we consider stars instead of trees, a static, infinite universe would have a star everywhere we look, and the night sky should not be dark. The distant stars would be dim, but each distant star would cover just a small angular patch of sky. While the intensity of light falls as the square of distance, the surface area of a sphere at that distance is larger by the square of the distance, so there would be just as many stars on that sphere's surface to compensate.

This is called Olbers' paradox, named after the German astronomer, Heinrich Wilhelm Matthias Olbers (1758-1840), although Olbers wasn't the first to have this idea. Of course, to even reach the point of Olbers' paradox, astronomers needed to abandon the ancient conception of the stars being fixed on the surface of one, huge celestial sphere.

German astronomer, Heinrich Wilhelm Matthias Olbers (1758-1840).

Although Olbers' paradox is named after Olbers, who stated it in 1823, many others deserve some credit, including Kepler, Halley, and Cheseaux. Kelvin, who had opinions on many scientific matters, gave one resolution of the paradox in a 1901 paper.

(Lithograph by Rudolf Suhrlandt (1781-1862), via Wikimedia Commons.)

Since the night sky is dark, there must be something that prevents the light of distant stars from reaching us. The first possibility is that the number of stars is finite, and this was Kepler's argument. In fact, as late as the first part of the 20th century, many astronomers still believed that our Milky Way Galaxy was all there was to the universe.

Jean-Philippe de Chéseaux (1718-1751) and Kelvin suggested that the finite lifetime of stars gave us dark night skies, but it's known that star formation occurs, and this maintains the number of stars. Cheseaux, along with Olbers and Halley, thought that obscuring dust clouds might be the explanation. After a sufficient time for thermal equilibrium, the dust clouds would glow as brightly as the stars whose energy they absorbed, so this explanation fails.[3]

Our present knowledge of the universe presents two other solutions to Olbers paradox. Since our universe has had its origin in the Big Bang, we know that it doesn't have an infinite age. Furthermore, universal expansion causes a redshift in distant light, and that removes it from the visible spectrum. However, don't be fooled into thinking that dark matter might have a role. Dark matter is dark because it neither emits nor absorbs electromagnetic radiation .

My favorite representation of the sphere of the fixed stars. It's human nature to want to see past phenomena to their cause.

(Woodcut from Camille Flammarion's, L'Atmosphere: Météorologie Populaire (Paris, 1888), p. 163, via Via Wikimedia Commons.)

Although intergalactic dust is not the solution to Olbers' paradox, dust within our own galaxy has a tremendous affect on the number of visible stars. The galactic plane is full of dust, and one significant dark patch is the Great Rift, a stretch of darkness that extends over a third of the galactic width. It extends from the constellation, Cygnus, to the constellation, Centaurus. This dark cloud is estimated to have a mass a million times that of the Sun, and other galaxies have similar dark bands.

A particularly opaque patch of interstellar dust, dark nebula LDN 483, has been photographed by the European Southern Observatory's 2.2-meter telescope at the La Silla Observatory in Chile.[4-5] LDN 483 is about 700 light years distant, located in the constellation, Serpens (see figure).

The red circle shows the area of the dark nebula LDN 483, pictured on the right by a wide field image from the MPG/ESO 2.2-meter telescope at the La Silla Observatory in Chile. (Left image, star chart from KStars; right image, ESO.)

LDN 483 completely blocks the visible light from background stars. Such dark patches are actually nurseries for the development of young stars. Such stars form by the gravitational coalescence of the dust into a ball of material that eventually heats as it densifies under gravitational collapse.

The progress of such star formation can be tracked by imaging their emitted radiation from microwave, through infrared, to visible light. It's estimated that LDN 483 will disperse, lose its opacity, and reveal the obscured background stars in a few million years. Then, the light of these background stars will be joined by the light of the new stars formed in the cloud.[4]

Olbers' Paradox

References: