This article on Olbers’ paradox is a guest article by Pratishtha Rawat, a student from the University of Geneva, Switzerland, pursuing her Master’s in Astrophysics.

One of the most popular paradoxes in astronomy starts with a fairly easy observation. Stars are bright. If you haven’t guessed it yet, we are talking about Olbers’ paradox. Olbers’ paradox, though formally named later, dates back several centuries. It questions how a uniformly distributed, static universe full of bright stars can have a dark night sky. If the universe were indeed infinitely full of these luminous objects, as assumed at the time, all lines of sight would trace back to one star or the other – causing a magnificently bright sky at all times. 

Evidently, that’s not the case. The night sky is dark.

How A Simple Night Sky Observation Turned Into One Of The Most Popular Paradoxes In Science. 1
Olbers’ paradox is one of the most interesting paradoxes in astronomy

Why are stars bright?

Before we proceed to detangle Olbers’ Paradox or question our observations, it is curious to note that neither of these was stipulated after discovering the mechanism of nuclear energy. This meant that scientists could speculate other reasons that caused the brightness of stars. And it is a wonderful coincidence they did because it is, in fact, another phenomenon that causes the stars to shine! This is famously one of the problems where a neophyte has a better probability of getting the correct answer than an informed person. Though nuclear energy sustains the star, it is not what makes it bright. So why is a star bright? 

The answer, surprisingly, is too simple. A star is bright because it is hot. The intense temperatures and pressures that give us the glowing, admirable spheres of gas are caused by gravity. As the stellar matter continuously collapses, the friction causes it to heat up. It is this heat and pressure, then, that allows the nuclear reactions to happen. These reactions are further responsible for thermal and radiation pressure in the star, attempting to push the stellar layers out to infinity. Intuitively, this seems non-ideal because if unregulated, we would expect this to disrupt the star!

Hydrostatic equilibrium – A natural balance

The kind of stellar disruption described above is something astronomers have seldom worried about because nature has a beautiful way of creating balance. As we know, stars are held together by gravity. This gravity counteracts the thermal and radiation pressure forces by compressing material towards the center. This balance between gravity and thermal pressure is known as hydrostatic equilibrium.

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Hydrostatic equilibrium also explains a few interesting things back home on planet earth – like how the tires on our bicycles can support our weight. But, returning to stars, should we expect a disruption when one of the concerned forces becomes greater than the other? Nature again denies such an imbalance as hydrostatic equilibrium in stars is a self-regulating mechanism. This means that if the rate of nuclear energy generation in the core slows down, gravity dominates the pressure, and the star begins to contract. This contraction increases the temperature and pressure of the star’s interior, which leads to higher energy generation rates and, therefore, a return to equilibrium.

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Inversely, if the fusion rate increases, the core will expand under greater thermal pressure. This would decrease the temperature and density, reducing the fusion rate and directing the star back to equilibrium.

The role of nuclear reactions

What if we didn’t have nuclear reactions for equilibrium, to begin with? We have already established that a star can be bright just with gravitational compression, then are nuclear reactions mandatory for the bright gaseous spheres we see? If not, does that mean we can have a star without nuclear reactions? Well, yes, it does! If a short-lived star is what’s needed, gravitational collapse can give us the brightness we see. But for stars to continue to shine like we watch them do, nuclear reactions come into play.

As collapse occurs, heating facilitates the beginning of nuclear reactions that continue to generate energy for the star (curious note: a star is said to be “born” when nuclear fusion reactions begin). Typically, a star like our Sun can take approximately 20 million years to reach the stage of nuclear energy generation. However, once it does, nuclear fusion can power it for around 10 billion years! 

Besides being the sustaining mechanism for stars, nuclear reactions are important because they affect the evolution of a star and even the observations we make. At this point, you may question how do reactions in the core influence our observations or whether these observations are different from the light we see every day. Indeed, they are.

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The light we see comes mainly from the Sun’s surface. If we wanted to record the light coming from deeper regions, say the core, it could take up to 200,000 years to get the light to the surface of the Sun. It is like walking across a very crowded room. A photon trying to make its way out of the core would constantly be interacting with particles in the packed, dense core – getting absorbed and remitted before reaching the radiative zone from where it can finally escape to reach us. 

Shedding some light on the mystery of darkness – The Olbers’ paradox

Having addressed the origin of some photons and the escape of some others, let’s circle back to discussing several of such escapes from several sources – the Olbers’ paradox. An infinite number of sources shooting photons in our direction, how does that permit the sky to have darkness at all? 

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The catch isn’t in quantifying the number of sources to a huge number and calling them finite. The catch is in the speed of light being finite. Even an infinite number of sources cannot instantaneously transport photons to the Earth if the speed at which they travel is finite! Neither is the age of the universe we reside in infinite to help the photons travel at the speed of light enough time to reach us.

Thus, there is only a finite universe that we can observe, constrained by the present age and the finite speed of light in it. This causes light emitted from stars at distances greater than the radius of our visible universe not to be received, thus causing the night sky’s darkness. The solution to the paradox interestingly supports the big bang formulation of the universe, much like Bentley’s paradox has earlier supported an ending in the Big Crunch. It is a wonderful present to learn about the power of paradoxes, isn’t it? 

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