How to Measure the Universe’s Size by Simply Looking into the Night Sky

Aim / Overview

This activity introduces Olbers’s Paradox and shows that the Universe must either be finite in size, or have a finite lifetime. Simply put, it proves either than the Universe does not “go on for ever” or “has not been there forever”. This is a profound observation, and the knowledge that we can prove this simply by looking into the night sky (or even the day sky, for that matter as should become clear) without instruments is something children find fascinating. You can’t of course come up with “so many kilometres”, or “so many billion years”, but to scientists the fact of a finite universe (either in time or space) is the far more important information.

Materials

One or more curious child / children.

Optional: (i) One forest, or (ii) enough exercise mats for each child to lie on and a quiet room to do the activity in.

This is a “Thought experiment” where we ask ourselves “what if?” and work things out by seeing how Nature answers these questions (i.e. by squaring our thoughts with reality). This thought experiment can be done anywhere, but is particularly poignant if done whilst on a walk into a forest just as one is leaving the edge of the forest and can still see houses and other things on the outside. Another way to strengthen the effect might be to have the children lie on exercise mats, shut their eyes and relax whilst you weave a little story for them with the relevant questions along the lines of my story in the next section.

The Experiment

Imagine we are walking into a forest. We are leaving a little town, or maybe a carpark, or maybe a picnic area on the forest’s edge. We look back over our shoulder from time to time as we go.

So we walk a few hundred steps and look back over our shoulder. What do we see? We can still see the people and houses outside the trees, but here and there trees block our sight, so we see a village scene striped through top to bottom by the treetrunks.

We walk further, looking back as we go. The treetrunks encroach the village scene more and more, but we can still see the odd splash of colour here and there: the bright flowers on a little girl’s dress as she scurries delightedly after her little brother, who is wearing a rainbow sunhat, and we hear their shrieks of delight in the distance. Now and then our eyes catch the glint of passing cars as they jerkily run across our treetrunk-punctuated field of view. The hubbub and business of the villagers is a faint buzz, even the violence of the shouts of two fellows we passed at the forest edge arguing about a carpark one thinks the other stole from him is softened into a pleasant, mossy sound.

We walk further and further, the sounds of the forest birds slowly wipes the village away and after maybe a half an hour we reach a sunny glade near a creek, with some smooth rounded stones that look just the right height and shape to sit on and take the forest’s thriving lifesounds in from.

The Question

Now what do we see? And why? Can we tell how far into the forest we are, only by looking out from our glade?

We imagine now, if we can, that the forest were infinite and that our sunny glade with its creek bearing fishes and yabbies and other food is our true home. We have always lived here in this beautiful glade. For most of our lives we believed there was nothing else in the World but our glade and the hint of otherworldliness from the foreboding sight of trees that surround us. But just recently we have boldly ventured out, a tiny few steps, into the forest around our home. Some brave souls say they even went so far into the woods that they could see nothing but trees. All around them there were birdsounds and darkness and no hint of how to get home. They proudly brag that they did get home thanks to some oh so very clever technology they have recently invented and used to tell them always which direction our life giving glade lay in.

How do we think the view from a glade in a neverending forest would differ from the real one we are in, only a few kilometres from the noisy village?

Now we think about the real night sky. Is altogether dark? Is it bright? How would we describe it? What about:

It’s dark with twinkly bits sputtered through it, and here and there weird, softly glowing clouds.

For me at least, it’s hard to think of a better one-sentence description of how the night sky looks. So, thinking about our forest and imagining instead a forest of stars rather than treetrunks:

What should we see in the night sky if the Universe were truly neverending, or at least very, very big?

Discussion and Afterthoughts

The children by this point should have noticed a clash, or contradiction, between what their thought experiment foretells and what reality is. If the Universe were truly infinite, the sky would be ablaze with light. There would be no dark spots anywhere. Everywhere we looked there would be a star. Indeed, from the science of thermodynamics we know our Earth would be in thermodynamic equilibrium with all the stars’ surfaces. This means it would be hot here. Blazingly hot. Hotter than the hearth of the most ferocious kiln you can think of – at least as hot as our Sun’s surface, which is about six thousand degrees Kelvin (which is pretty much the same as degrees Celsius at such high temperatures).

Indeed there could be no life as we know it. The Earth wouldn’t even be here. Nor even would any other planets. They would have melted and seethed into an ionised gas strewn far and wide throughout interstellar space long ago!

This is Olbers’s paradox, and we (humans) really only understood what it means a mere hundred or so years ago. We think we are oh so very clever, but a hundred years is only a tiny fraction of the time we think of ourselves as having been civilised for. To help understand Olbers’s paradox, you can use the evocative little gif loop from the Wikipedia page for Olbers’s Paradox.

Olber's_Paradox_-_All_Points

Here are some questions to explore with the children.

  1. So why isn’t the sky blazing with light at all times?
  2. Going back to our forest story, when could we see both trees and outside the forest?
  3. So, maybe we’re at the edge of the Universe. How do we know this can’t be so? Our view of the night sky is such that we can see dark with twinkly bits in one direction: if we were at the edge of the Universe, what would we see as we turned around and looked in the opposite direction? How would we look into the opposite direction? (Hint: You’d need to wait half a year). After half a year, do we still only see dark with twinkly bits?
  4. What if the Universe had an ending. Beyond a certain distance from us, there are no stars. Would that explain what we see? Would that explain dark with twinkly bits?
  5. What if the Universe were infinitely wide (you can go as far as you like and never reach a boundary), but had only lived for a relatively short time? We know that light doesn’t go infinitely fast – it takes about a tenth of one second to go around the Earth, a little over a whole second to reach the Moon, eight minutes to reach the Earth from the Sun, twenty minutes (give or take) to reach Mars, roughly four hours to reach Neptune, the outermost planet in the Solar System and four years to reach the nearest star to Earth (Proxima Centauri) aside from our Sun. What if the stars had only switched on a “short” time ago?

So we see from the simple fact that our night sky is dark with twinkly bits in it, we can prove that the Universe either cannot be infinitely wide, or stars cannot have been glowing forever. The Universe must be finite in space, finite in time or both.

Modern astronomers are almost certain that the Universe has “only” been since about 13.7 thousand million years ago. Many experiments give this number.

So, right now, we don’t know whether the Universe is infinitely wide. We can only see a certain limited region in this expanse because our best theories suggest that light is the fastest thing in the Universe. So we can only see things that are at most 13.7 thousand million years old. Actually that doesn’t quite mean that the observable Universe is 2×13.7 = 27.6 thousand million years wide. It is most likely that space itself has been stretching over time! But this is roughly the right idea. When we take into account that space has been stretching, the observable Universe is between about 50 and 150 thousand million lightyears across, depending on what numbers scientists put into their calculations. When you are taking observations from only one point in the Universe, we’re not to certain of many of the values we should be using in calculations. There are some (indirect) experimental data which suggest the Universe may be very much bigger than we can see. See for example the Wikipedia page for Observable Universe.

So, merely by looking at the night sky, we can tell that the Universe must be finitely wide, or must have lingered only a finite time, or both. What an astounding thing to find out by such a simple observation!

Some history:  It is highly likely that the first person to discover this amazing fact was Edgar Allen Poe. He proposed a solution (finite size) in a poem called “Eureka”. Although Edgar Allen Poe was an amateur scientist, he is much more famous for being an author of macabre mystery and horror stories and poems. So not many scientists took his work seriously and indeed “Eureka” contains many ideas which even then were in stark disagreement with known facts.

 edgar_allan_poe_by_crisvector-d3jswe4

The first mainstream scientist to resolve the paradox was Lord Kelvin in 1901. However, with the coming of General Relativity, Hubble’s law and the Big Bang theory, not even the assumptions of finitely wide or finitely old are enough to resolve the paradox, whose resolution in modern science is quite technical. However, we still need at least one of these assumptions as well as other cosmological technicalities to explain the paradox, so our central point still stands: that the night sky is dark with twinkly bits proves our universe must be either finitely wide or finitely old or both. We are fairly sure how old, we really have no idea about how big our Universe is!