What is reality? What is existence? These questions have bothered our species since antiquity. For thousands of years we speculated the nature of the Cosmos, coming up with the wildest of imaginations. But only recently, after the advent of the scientific approach of viewing things did we finally begin to understand the true nature of the Universe we inhabit. There is still a long way to go but till now, science has come up with some pretty interesting facts as it turns out, that the Universe at its most fundamental level runs itself based on a few numbers. That’s right… Just numbers.
Before we dive in, let me clarify what this actually means and why you or anyone for that matter must marvel at it. These numbers that we are going to discuss about are not just any other random numbers. They may look ugly, but trust me, this is what defines the Universe we live in. Were these values any different, then the Universe as we know it would cease to exist. Mathematics, the same old boring mathematics turns out to be the language of the Universe. It defines reality itself. Now all that might seem vague but after reading this post, hopefully you will realise that maths isn’t just playing with numbers as taught in most schools.
1. Pi = 3.141592…
Let’s start off with something that maybe very familiar to you. Pi also denoted as Π is the number you would get if you divide the circumference of a circle with its diameter. And this holds true for any circle, may it be the size of a pinhead or as big as the Sun!! The ratio of its circumference to its diameter would always be 3.141592… or in other words Pi. Basically that’s all what we are told about Pi which is quite saddening given the immense importance of this number in describing the Universe itself.
At first sight, a peculiar ratio on a plain shape like a circle seems little of importance when describing a whole Universe, but nothing could be further from the truth. We know that pi also shows up when calculating the area of a circle (Πr2) and volume of a sphere (4/3Πr3) and this very fact is what shows up in Einsteins equations which describe the very curvature of space. The theory of relativity states the gravity is a by-product of the curvature of space itself around and object. When an object falls to the ground, it’s not because of some invisible force, but because space itself is bent.
This curvature is uniform in all directions which forms a sphere and as you might have already guessed a sphere means there has to be pi involved. And surely enough the equations that describe the curving of space contain pi. However we won’t get into the math here as that would lead us somewhere far from the main focus of this post.
So there you have it, the very fabric of spacetime bends according to the value of pi, a simple number that we use all the time, especially in school exams when dealing with common day shapes like circles.
2. The Universal Gravitational Constant = 6.67×10-11 Nm2/kg2
You have probably heard of this one too. Also written as G for short, the gravitational constant appears in Newton’s equations and describes the gravitational attraction between masses. This equation is something you might probably remember from high school physics class:
The technical definition of G is that it is the value of the gravitational force of attraction between two bodies of 1 kg mass separated by a distance of 1 meter. It has a very small value of 6.67×10-11 Nm2/kg2. The ‘universal’ in the title might have probably told you that this value is constant throughout the Universe.
The fascinating fact about this number however is that it shows the weakness of the gravitational force. What do I mean by that? Well, consider an apple lying on the ground and you pick it up. Just now, by lifting that apple, you overpowered the force of the entire planet Earth trying to keep the apple on the ground. Although we do not know why gravity is so weak (although it should be if we want to exist) the small value of G is a gentle reminder of the fact that this is so. Try it yourself; plug-in the values for the mass of the Earth, the apple (say 500g) and the distance between the two in the above equation. You will see that even though the Earth is very massive, the extremely small number G, cancels out most of that and the force on the apple comes out to be only a couple of newtons.
Thus the force of gravity which keeps from flying off into space, the Earth in orbit around the Sun and the entire galaxy together all comes down to the value of a single number; a very small number indeed.
3. The Speed of Light = 299,792,458 m/s
Light is fast. In fact it is the fastest ‘thing’ in the entire Universe. According to Einstein’s Special Theory of Relativity nothing can travel faster than light, not even light itself. Moreover, light can travel only at one particular speed, not faster nor slower. That is at 299,792,458 m/s which is quite fast. It is so fast that light can travel 7 times around the globe in just one second!! Denoted by ‘c’ this number holds the same value throughout the Universe. But this speed is more than just a speed; it maintains the causality of the Universe itself.
To make things simple let us understand what causality is. Complicated as it may seem, causality just implies that cause comes before effect. This is pretty intuitive. We all know from day-to-day experience that for some event to have any effect it must be caused. You cannot have an effect before any event being caused. But if there was no limit on the speed of objects, you could in theory have effect before cause and this is something the Universe doesn’t like.
How? That’s because of Einstein’s Relativity again. Albert Einstein discovered that as you get closer and closer to the speed of light, time slows down for you. So if you are travelling very close to the speed of light in a spacecraft, 1 second for you might be a couple of days for someone back on Earth. This effect gets stronger as you approach light speed closer and closer. When you hit light speed however, time stops (whatever that means). This is where the key lies. If we continue this trend, time would actually run backwards once you begin to move faster than light. So if you set off on a rocket faster than the speed of light to Jupiter and returned, you could travel backward in time and reach before you even left. This gives rise to all sorts of crazy paradoxes which break causality (here effect of you returning happens before the cause that is your departure). This is why travelling faster than light is a complete no-no. No matter how fast you accelerate, you will never hit the speed of light although you could get very close.
There are various other mind bending effects of travelling at light speed but that is not the theme of this post, hence we won’t be talking about it. The main goal here is to show how these constants shape our very existence which would not be possible if people could return from their vacation before they left!!
4. The Fine Structure Constant = 1/137
We all know that we and everything we see in the Universe is made up of atoms. Atoms are made of electrons and protons which are further made of quarks. As subatomic particles form the basis of all matter in the Universe, their interactions play a key role in how our Universe is shaped. Most of these interactions occur according to one of the 4 fundamental forces of Nature: Gravity, Electromagnetism, the Strong and Weak Nuclear forces.
Our interest here lies in electromagnetism which is responsible for the electricity in our house, the working of magnets and the stability of the atom itself. Like all other forces, this force is also mediated throughout the Universe by a field. For electromagnetism it’s called the electromagnetic field. There are various equations which describe how electrons and other particles interact with this field. Amongst the ugly mess of equations which I won’t bother to write here (thank me later, math haters) one number plays a key role in describing the interactions. Called the Fine Structure Constant or α, it has a value of 1/137.
This number is one of the most fundamental properties of the Universe. It is this constant which describes the structure of atoms, bonding of molecules, stability of stars and basically the structure of the Universe. Moreover it is so delicate that if the value was a little different (even by 4%) stars would not form, atoms would crumble and the Universe as we know it would not exist. That is mind-blowing… As a fun fact, this number is so fundamental to our Universe, we could use it as a signal aimed at outer space which could help us showcase our presence as an intelligent civilisation to aliens, if any out there.
5. The Planck Constants
At number 5 we have not one, but a group of constants all related to the quantum level of the Universe discovered by physicist Max Planck (hence the name). These numbers appear a lot in quantum mechanics which is one of the 2 main pillars of modern-day physics. To begin with, we will start with the most important of all: The Planck’s Constant also denoted by h. With a value of 6.62×10-34 J/s the Planck Constant describes the relation between the energy of a photon and its frequency. For those of you who had paid attention during your physics lectures in high-school, the precise equation concerning this is:
where E denotes the Energy and ν denotes frequency. Again, you might have seen this formula in high school classes but we are here not to revise all that, but to see the elegance behind these numbers. The seemingly drab Planck’s constant actually may put an end to Zeno’s Paradox by introducing some quantities that are the fundamental bits of the Universe. As a refresher, Zeno’s Paradox is based on the idea that when you approach an object, you could never really reach it because the distance between you and that object will continue to become smaller and smaller but it could never become zero. We know that this doesn’t happen as we do reach objects. So what’s the catch? Enter the Planck Length.
The Planck Length is what puts the limit to how small something can get. It is the smallest possible length in the Universe and it is incredibly small with a value of 1.6×10-35m. That’s one billion billion times smaller than a proton!! Of course one can ask why can’t something be half that size? We can’t answer that question with. certainty as we don’t have powerful enough instrument yet to probe these small distances. However anything smaller than the Planck Length is meaningless in quantum theory. This brings to other Planck quantity
Planck Time is the time taken by light to cover the Planck Length. Like the Planck Length, the Planck Time is the smallest unit of time with a value of 5.39×10-44s. Just think how small that is. It is the time light, being the fastest in the Universe, which can cover the Earth 7 times in a second, takes to cover a distance a billion billion times smaller than a proton!!
All these quantities define the basic bits of space and time itself and hence are very important in the study of the Universe. They could one day reveal the building blocks of reality itself. And how do we derive these values? Through the Planck’s constant (h). Although I won’t mention the actual equations here, it is enough to understand that the Planck’s constant plays a key role while obtaining values for the Planck Time and Length.
6. The Golden Ratio = 1.61803…
No list of fundamental constants would be complete without this one. The Golden Ratio, a number so weird, that we don’t even know what it represents in the Universe. At first glance 1.61803… might seem like any other number. But it’s not; because it’s the Golden Ratio (denoted by φ) and it is found almost everywhere in the Universe. Let us make ourselves clear first. To understand where exactly this number pops up, take a look at a pinecone and observe its arms as shown in the diagram.
A pinecone has two sets of spiral arms running in opposite directions. If you divide the number of arms of the bigger spiral with the number of arms of the smaller one, you will get a value close to the Golden Ratio. This does not work only for pinecones, but for sunflowers as well!! In fact you should try it out; go find a flower and try to identify the two spirals in its seeds and perform the above experiment. But it doesn’t end there. From seashells, hurricanes to entire galaxies exhibit this ratio in some form or the other. The ratio of the length of the human body from head to naval to the length from the naval to the foot comes close to the Golden Ratio!! This number exists in you too and the best part is you can verify it!!
We won’t be able to discuss everything about this number in this post alone due to the sheer amount of information it holds which may sidetrack us from this post. So if you are interested, you can check out my post dedicated entirely to this number over here.
The weird part though is that we do not know why this number appears in Nature so often. We don’t know what it represents, what it is and why it is? However it sure holds a key to the workings of the Universe and hence is worth mentioning.
And there we have it. Some of the most Fundamental Constants to Reality. I haven’t included numbers like Euler’s Number (e) or the Electric Constant (k) as these are not fundamental to Nature itself. Some are defined by human measurements and convention, while others hold different values for different mediums.
However the ones mentioned above play a key role in shaping reality itself and it is due to them that the Universe behaves the way it does. Think about it. The Universe defines itself through numbers, the core of mathematics. A subject that receives a lot of hatred at school is the reason for your existence and defines your existence. So next time you curse at ugly looking numbers in your textbooks remember, if it wasn’t for them… you would be dead!!
17 thoughts on “The Fundamental Constants of Reality”
Too heavy for me. But quite a detailed write-up.
I find the golden ratio and the fine structure constant the most fascinating.
Keep the articles coming. They are very interesting.
Thats an excellent article. Was great reading about the numbers that define our very existence. I would personally like to read more articles about time , space and the theory of relativity.
Awesome, shed light on something one wouldn’t remotely give a thought!! Thanks for highlighting it Aryamann!
Aryamann, your passion has given you a comprehensive and indepth understanding of the subject, best wishes for a brilliant future
I would definitely say well written. Couldnt imagine myself writing this at this age 😁.
Brilliantly written !! articulate, lucid and just the right level of complexity for the rest of us to be able to understand !! kudos !!
Excellent Aryamann. Keep it up. Wishing you a great future as it’s extremely difficult to master such knowledge without in-depth commitment and passion
Very informative article with a good narrative. Keep it up Aryamann
Aryamann, your write-up regarding the constants is just brilliant and spell bounding. Waiting for more blogs in the future.
Great job Aryamann! Interesting explanation of the fundamental constants and it’s importance.
Look forward to your articles.
Great job Aryamann! Interesting article about the fundamental constants and it’s importance.
Look forward to your articles.
Wonderful post!! Well done, Aryamann! I’m amazed at the way you’ve explained each of these mind bending concepts so lucidly. It’s testament of the fact at how well you understand the subject and how well you relate to the universe around you. Secondly, the way in which you have captured the attention of the reader is worth putting in the introduction section of an intermediate level high school textbook. Keep up the great work! I’m sure your blog will be wildly popular for the average reader one day! Until then, keep the posts coming…
A v.good write up on a mind boggling subject v.few would understand. The concepts are well explained & lucid so that even a common man can understand. This only shows the in depth knowledge & passion that you have in the related subject. Keep the good work coming, Aryamann.
Very informative! Very well written in simple terms which makes it easy to grasp . This shows your depth of knowledge. If only you were my physics lecturer at school I’m sure I would have done better.
Do keep the posts coming .
Well done. Thank you.
Read it the third time and found it as interesting as the first.