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09 December 2013

Olbers’ Paradox and Electromagnetic Waves

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Olbers’ paradox is a seemingly innocent question posed by the German doctor and astronomer Heinrich W. Olbers (11 October 1758 – 2 March 1840) circa 1820: if there is an infinite number of stars, why is the sky dark at night rather than bright?

However, it was not an innocent question. It is so profound that it has not been answered satisfactorily until we had the cosmological view of the 20th century. At the beginning, not much attention was paid to this paradox because it seemed obvious that, if the sun does not shine at night, the sky would be dark. It was later theorized that, even though there were countless stars, their number was not infinite and there were therefore dark areas between them. In addition, because they were separated by vast distances, their light was very dim. It was also thought that there had not been enough time for the light of the more distant stars to reach us or, perhaps, that some kind of fog or cosmic dust stood between the stars and our planet.

The right answer presupposes the knowledge of two major events that have not been known until the 20th century. First, the existence of a big bang that originated our Universe some 13,700 million years ago and, second, that the Universe is expanding at an increasing rate like a balloon inflated at high pressure.

The implications of the latter require prior clarification. Energy is transported by the vacuum and by the air through electromagnetic waves, which are characterized by three aspects: their amplitude (distance between the crest of a wave and the trough of the next one), their length (distance between two crests or two troughs) and their frequency (number of waves per unit of time). All electromagnetic waves have the same amplitude and they only differ in terms of their length and frequency. The higher the frequency, the lower the wave length, and vice versa.

The collection of electromagnetic waves (the electromagnetic spectrum) is classified from longer to shorter wave length into: radio waves, microwaves, infrared light, visible light, ultraviolet light, X rays and gamma rays. The shorter the wave length and, therefore, the higher the frequency, more and more energy is transported by the waves. Gamma rays are the highest-energy waves.

Our retina is designed to see visible light frequencies only. When a moving luminous object moves away from us, the waves “crowd together” or become narrower in the direction in which they are moving (their wave length decreases and their frequency increases), while in the opposite direction, i.e. when they move toward us, the opposite  (their length increases and their frequency happens). This is known as “Doppler effect” and is similar to what happens with the sound waves produced by a vehicle with a siren that moves toward us and then moves away. First, the tone becomes high-pitched and then low-pitched.

When a luminous object moves away from us, its light spectrum (i.e. the set of frequencies of the different colors of visible light) “drops” or moves toward the infrared sector, and if the object’s speed is high enough, at some point that light is no longer visible to the human eye.

We will now go back to Olbers’ paradox. When we look at the sky we are looking back at the past. The sun’s light, for example, tells us how the sun was 8 minutes ago (the time it takes for its light to reach us). If the sun’s light went out suddenly, it would take us eight minutes to notice. If we see a celestial body that is at a distance of two million light-years, we are actually seeing how that object was two million years ago, and so on.

After the big bang, for approximately 350,000 years, the expanding Universe was superheated plasma at around 3,000 degrees Kelvin (above absolute zero), which was opaque, like very thick fog. The protons, neutrons and electrons had not yet combined to form the first atoms and the light could not slip through them. So, if we keep looking at the sky farther and farther away, at a distance of about 13,000 light-years, we will see the Universe at a point in time when it was opaque and dark. If it had emitted some kind of luminosity, the edge of that Universe and its nearest objects would be moving away from us at such a high speed that the light would have moved completely toward the infrared or microwave band, and would therefore be invisible to the human eye.


For the two reasons set out, the night sky is dark. The background of space is black and, moreover, the first visible light will have now moved at least to the infrared band. In fact, since 1965 it is known that the cosmic background of radiation is a microwave background at a temperature of 2.7 degrees Kelvin and is identical in any direction in space. In a way, it is like the “noise” that remains from the great big bang. Naturally, this microwave radiation is not visible to the human eye and can only be detected using special antennae.

Ramón Reis

Economist, Madrid (Spain)

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