If our universe is infinitely old and infinitely large, then why is the night sky so dark?
This is Olbers' paradox, named after german astronomer Heinrich Olbers (1758-1840). First proposed by Johannes Kepler (1571-1630), the argument is as follows:
An infinitely old and infinitely large universe would have an infinite number of stars.
Therefore, every time you looked out into the sky, your line of sight would always, eventually, meet a star (like standing in a dense forest: everywhere you look, your eye meets a tree).
An infinite number of stars, filling every nook and cranny in the sky, would make it bright.
But the night sky is not bright. It's dark... So what's going on?
Lots of astronomers made suggestions, including Olbers, who believed that most of the starlight was getting absorbed on its way to us. But it was writer Edgar Allen Poe (1809-1849) who first came up with the correct solution. He suggested that the universe wasn't infinitely old, but instead had a beginning. This means that starlight from the most distant stars hasn't had time to reach us yet!
Aside: Edgar Allen Poe discussed his solution to Olbers' paradox in his "Prose Poem"Eureka. The relevant passage reads as follows:
âWere the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy -- since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all."
Eureka, a lengthy commentary on the spiritual and material universe, was published the year before Poe's death. Without any scientific evidence, as such, to support his essay's claims, Eureka makes some spooky (for want of a better word) assertions about astrophysical and cosmological phenomena that were yet to be formally discovered at the time of its publication.
Eureka can be read in full by clicking here. Alternatively, if you want to learn more about how certain quotes from Poe in Eureka relate to modern science, I'd recommend clicking here, or here.
Astronomers today calculate that the universe began 13.8 billion years ago. Modern humans have only walked the Earth for less than half a million years. That means that we've only existed for the last 0.00004% (oops! I missed off two zeroes here during my TikTok. Apologies!) of the universe's entire life.
So that's Olbers' paradox solved! It turns out that the universe is not, in fact, infinitely old...
I had so many interesting and thought-provoking comments and questions on this TikTok. Amongst them, there were quite a few recurring themes that I think are worth some discussion:
Before we jump in though, I did have a lot of comments telling me that the night sky is bright, and if I left the city I'd realise this. I understand what these comments are trying to say. But Olbers' paradox implies that the sky should be a solid "wall" of starlight in every direction, all day and all night. I hope we can all agree that that's not the case, even from a desert island as far away from civilisation as possible!
I also had quite a few comments mentioning flawed assumptions. For example:"but we already know that the universe isn't infinitely old". Yes, of course, this is true today! But it hasn't always been this way. In fact, the very point of this video was to illustrate the journey that we've been on to change our views about the nature of the universe. The belief that the universe is eternal and unchanging was commonplace until fairly recently. Olbers' paradox is the logical wrestling match between this belief and observational evidence, and Edgar Allen Poe's solution was considered radical at the time. In fact, it wasn't until the mid-twentieth century (one hundred years or so after Poe's Eureka) that the "steady-state" model of the universe was conclusively replaced with our current "evolving universe" model.
1. Why does an infinitely old and large universe have to mean a bright night sky? Surely far away stars would still be so dim they aren't detectable with the naked eye?
This boils down to the mathematics of the paradox:
The further away any object is from an observer, the dimmer it appears.
The exact relationship between distance and brightness is an "inverse square law", i.e. an object twice as far away appears only a quarter as bright.
As we look out into the sky, we are looking into a series of concentric spherical shells surrounding the Earth, at a series of increasing distances from us.
The equation for the surface area of a sphere means that the surface area of these shells will increase with the square of their radius. Provided the density of stars in the universe remains constant, then the number of stars in each shell will also increase at the same rate.
Therefore, with each increase in distance, the decrease in stellar brightness of each shell will be completely offset by the increase in surface area.
This results in a sky that should be as bright as the Sun, as viewed from Earth.
I've included a visualisation of this idea below:
2. Is there really no other solution?
2.1 What if, even if the universe itself is infinite, the number of stars within it is finite?
Here we are assuming that with an infinite universe comes an infinite amount of energy and an infinite amount of matter, spread evenly across it. Therefore an infinite universe cannot have an finite number of stars.
2.2 Could the finite lifetime of stars not explain things?
Infinity is an odd concept to get one's head around. But if there were infinite stars in the universe for an infinite time, then an infinite number of those would always be alive, and a further infinite number would always be dead. So the finite lifetime of individual stars would actually have no consequence!
2.3 What if loads of the starlight is absorbed on its way to us by dust, planets, or even black holes?
A good point, so good that it was the solution that Olbers proposed himself. So what's wrong with this idea?
The first law of thermodynamics (otherwise known as the conservation of energy) states that "energy cannot be created or destroyed".
The second law of thermodynamics is a bit more complicated, but can be partially explained by the following expression: "heat transfer occurs spontaneously from higher to lower temperature bodies, but never spontaneously in the reverse direction".
In this situation, these two laws combined translate as"what is absorbed must be re-radiated".
Therefore, even if almost all the light between distant stars and us were absorbed by objects in the way, eventually that radiation has to be released again (even black holes slowly re-radiate absorbed energy, in the form of Hawking radiation). This means that on an infinite timescale, the energy reaching us on Earth would still be the same, and the sky still should glow brightly. As this website puts it, it would be like throwing dust into an oven and expecting it to cool down.
2.4 What about if the universe is not infinite in size instead?
This, of course, would work as a solution too! It's just that we now have lots of evidence supporting the idea that the universe has a finite age. So, that actually solves the paradox on its own, without needing to worry if the universe is infinite or finite in extent as well.
This is quite lucky really, because it turns out we can't prove the size of the universe. This is because the universe's age, coupled with the finite speed of light, means we can only see so far: out to the distance that light has been able to travel during the universe's existence.
This bubble around us is known as the "observable universe", and we have no idea what's beyond the horizon. Even these experts couldn't agree on the extent of the rest of the universe beyond...
2.5 Could it not be that the night sky is bright with starlight from an infinite number of stars, just at different wavelengths to the ones we can see?
For those that are unaware, we can only see a tiny fraction of the "electromagnetic (EM) spectrum" of light. Beyond the part of the spectrum that we can see, there's infrared light, microwaves, and radiowaves, each with wavelengths longer than visible light. There's also ultraviolet light, X rays and gamma rays, each with shorter wavelengths than visible light. The wavelength of light is associated with how much energy the light has, with shorter wavelengths holding more energy.
Interstellar dust, for example, which is a big culprit for absorbing starlight, re-emits the light it absorbs in the infrared part of the spectrum. Furthermore, a phenomenon called "redshift" states that the faster an object moves, the more stretched the light emitted from it becomes. Therefore, the light from the most distant stars, which are rapidly moving away from us as the universe expands, will have longer wavelengths than we can see.
Therefore, an argument can be made that perhaps if we design instruments that can "see" in longer wavelengths, we might discover the lost starlight from these infinite stars. The trouble is, we have such instruments, and whilst they have made incredible contributions to astrophysics (see below), they haven't discovered this missing light...
3. Hold on a second! The sky is bright at other wavelengths. What about the cosmic microwave background (CMB)?
This comment is really an extension of point 2.5 above. Many of you pointed out that we've discovered the sky is very bright in the microwave part of the electromagnetic spectrum. But the cause of this radiation at microwave wavelengths has nothing to do with starlight, and so isn't really relevant here!
Instead, this light is caused by something called the "cosmic microwave background (CMB)". This TikTok isn't about the CMB, so I'm not going to go into a huge amount of detail about it here. However, put simply, the CMB is like an afterglow of the Big Bang:
For the first few hundred thousand years after the creation of the universe, the matter and light created in the initial explosion could interact, and did so constantly. These early stages of the universe are often likened to some kind of soup, or opaque fog. However, as the universe cooled, the light lost energy and these interactions became less and less likely. Eventually, roughly 380,000 years after the big bang, they stopped altogether. This marked the creation of the CMB.
The CMB was very high energy initially, and so contained photons with very short wavelengths. However, over time, the universe has continued to cool, losing energy in the process. This has lengthened the wavelength of the CMB photons all the way to the microwave part of the electromagnetic spectrum.
4. If more of the distant universe is being revealed to us as time passes, does all this mean the night sky is getting progressively brighter?
This, I thought, was a fascinating question. To be honest, it was a question that hadn't crossed my mind before, and as such, was one I did not know the answer to. From a trawl of the internet, I think my response would be no, due to the following reasoning:
We don't live in a universe that is infinitely old with an infinite number of stars.
Furthermore, as we look out, we also look back in time (because of the finite speed of light). Therefore, when we look at distant objects in space, we aren't seeing those objects as they are now, but instead how they were millions or even billions of years ago.
This wouldn't matter if we lived in an eternal, unchanging universe. As we look back in time, everything would look exactly the same because nothing changes.
However, in the real, evolving universe, as we look back in time, we look further back into the primordial universe, before there were stars or even matter of any kind.
Therefore, whilst it's true to say that the edge of the observable universe is increasing with time and, as a consequence, more "stuff" is being revealed to us, This doesn't mean that the number of light sources in our sky will keep increasing as time goes on.
Furthermore, if we run the clock into the far distant future, the finite amount of matter in our universe means that, eventually, every star will die. Once this point has been reached, the night sky will turn to blackness and will be devoid of any signs of existence. But don't worry! We'll be long gone before then!
There are a few other subtle points regarding the answer to this question. However, I've chosen not to discuss those here. If you are curious, then this discussion thread is worth checking out!
For image credits, please see the image credits tab
Comments