Scales in the Universe

By | May 22, 2019

Most humans think that they are the centre of the Universe. While in one way, the way they want to believe it, may not be true, they may be right in another way. Let’s dig further and explore if this is really true.

We start by introducing the definition of a “metre”, a unit of distance. According to the International Systems of Units  (SI), symbol “m”, a metre is defined as a length travelled by light in a vacuum in \frac{1}{299792458} of a second. This unit is at the heart of all distance measurements (unless you are an American and prefer yards). When we are born we average at around 50 cm, or for consistency purposes, 0.5 m. An adult averages at around 167 cm or 1.67 m. Note that the adult height varies significantly between men and women and various other ethnic demographics, but for the purpose of this discussion we will assume it to be roughly 1.67 m.   

The Macro World:

Now we have all heard about heights of other things from time to time. For instance, the height of Minar-e-Pakistan (62 m) or the Eiffel tower (300 m) or the Burj Al-Arab (321 m). While these heights are all interesting, we would not be talking about these. These are all man-made structures. This discussion talks about “natural” structures. Examples of those would be K2 (8,611 m) and Mount Everest (8,848 m). While these things are large, at least by three order of magnitude, these lengths become miniscule when we start looking at heavenly bodies. The Earth, for example, has a circumference of 40,075,000 m, whereas the Sun has a circumference of 4,379,000,000 m. These lengths are six orders of magnitude larger than the height of the mountains. The number gets more crazier when we leave the atmosphere of Earth and get into distances (another form of length)  between heavenly bodies. For example the distance between Earth and Moon (384,400,000 m), Earth and Sun (149,600,000,000 m). At this stage the distances have started becoming so large that we need a new unit called the “Astronomical Unit” which is the approximate distance between the Earth and Sun. Remember these distances are all approximations because these orbits are not circular, but elliptical so all “single-value” distances are approximations. So, while we went by three order of magnitude between humans and mountains, we went up by a staggering seven to eight orders of magnitude between the mountains and distance between heavenly bodies.

Figure: The horizontal line indicates the order of magnitude (Log-like scale) of each of the objects pictorially represented alongside, as discussed in the post. The pictorial representation is not to scale.

One of the largest known stars, VY Canis Majoris, is 2,100 times larger than the Sun (in radius), which makes it ~1.93 * 10^{16} m in circumference. That is HUGE. However, the absurdity of distances does not end there. If you look out into the night sky, what you see is called the “Observable Universe”. The approximate diameter of the observable universe is 8.8 * 10^{26} m. This is just the “observable” which means that there may be more beyond that point. So before we go on, let us just touch on this subject. Light travels very fast. For instance if you turn on the button to a light bulb, current flows through the filament making it hot. The heat is radiated as light, which is almost instantaneous (in a manner of speaking, there is of course the time taken between the turning on of the switch and the heating up of the filament but lets discard that for now). The point is light travels fast. But if you start increasing the distance, light will start taking time to reach from one point to the other. For instance, if you shine a light at the moon and the moon bounces it back to you, it will take light 2.6 seconds to go from earth to the moon and back. The light from the Sun takes 8 minutes and 20 seconds to reach us. So here lies our problem. Light takes time to reach us from outer space. Light that reaches us from the edge of the “Observable Universe” is old. It is really really old. What we see today, left its sources ~15 billion years ago. Anyway, let us leave details of this for another post. For now, it is important to remember the upper cap of known distance at 8.8*10^{16} m. For our discussion, let us assume this value to be ~10^{27}

The Micro World:

Let us now start our journey in the other direction, that is into the world of the small. The first thing that comes to my mind are insects, like ants (0.005 m) and lice babies (0.001 m). Eventually all things are made up of cells, biological units of life which can be plant cells (averaging 100 um or 0.0001 m) or animal cells (averaging 0.00001 m) which comprise molecules (e.g. water 0.000000000275 m). While ants were three orders of magnitude smaller than us, and cells five, molecules are 10 orders of magnitude smaller than us. These are made of atoms, which are smaller still (e.g. Hydrogen atom, 0.00000000012 m). These distances can be simplified by writing them as 10^{-10} m.

Atoms were once thought of as fundamental particles, meaning that they could not be divided into smaller units and then along came the electrons, protons and neutrons. While electrons (10^{-16}m) are truly fundamental, protons and neutrons can be divided into smaller things (but we are not going to talk about the standard model of physics here), suffice to say that at the level of the electron, things are beginning to get really small.

Conclusion:

So, the largest object we looked at, VY Canis Majoris at ~1.93 * 10^{16} m and the smallest, the electron at ~10^{-16} m makes you wonder how the largest observed and the smallest observed things are nearly equally large and small. It should be noted that the size of an electron is not known, we just know that it is smaller than ~10^{-16} m, because that is the smallest we can measure. This also does not mean that it is the smallest object. Quarks are smaller (but that for another day).

So coming back to the point that if the largest (10^{16} m) and the smallest observable thing (10^{-16} m) are equally distant from us (10^{0} m), that is 16 orders of magnitude larger (+16) and 16 orders of magnitude smaller (-16), does not that make us HUMANS, “The centre of the Universe” in a manner of speaking?

Author Statement:

This post is co-authored by Yumna Majeed from Exploration and IDRACK.

Disclaimer:

This article is intended for children to make them think about large and small things. The dimensions used in this work are approximations and do not necessarily reflect accurate values, however care has been taken, where possible, that the magnitude of the values is preserved. All values were extracted from Google searches.

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