The Infinity Crisis
A number, a place or a finite within our minds? (Part-2)
“I am incapable of conceiving infinity, and yet I do not accept finity,” Simone de Beauvoir
Previously we discussed how infinity can exist mathematically and how calculus can put it to use. However, do these infinities exist in the universe we live? After all, the math gives a big thumbs up and anything that exists mathematically should exist physically as well. Imaginary numbers weren’t thought to be real yet they popped up in the Schrodinger equation describing real wave functions. In fact, complex numbers are an unavoidable part of our description of the physical universe. So let’s try to figure out whether the infinite infinity is a real thing or something that is a human invention for a very long time.
Can I someday wrap my arms around infinity and say, “Here it is! Here’s the infinite!”
Well, sadly the answer isn’t a yes this time. There’s simply no way that we can measure the infinite. Nobody would be able to give you the value of pi or root two to all of it’s infinite digits as the result of a measurement. The best we can do is make approximations. To understand this better, let’s talk about the continuum (Mathematicians are great in talking about it).
A Blob of Jell-O
Think of a piece of Jell-O, hanging out there, jiggling on a table. You obviously don’t picture it as being made of atoms; you just think it’s a continuum of uhh…Jell-O stuff. You think it’s infinitely subdivisible and has no gaps. It’s what the most of us (at least the normal ones out there) think stuff really is like.
So what is continuity? It is the idea that if you take a line, you can cut it in half, and then in half, and then in half again, and you’ll always have a line and you never stop, you just keep dividing stuff forever. Do you come across stuff like this in reality? Can you just take a rope and cut it in half forever? Welp, a piece of rope is not continuous…in fact no piece of matter is continuous. We do know that it’s made by individual pieces called molecules… or atoms… or electrons… or quarks. However this is not the continuity which is questionable. It is the continuity of space itself, not of matter. If you consider the space between your hands and divide it in half, can you go on forever?
Cutting Space (Literally)
If we take what we best know about the world, which is Einstein’s Theory of General Relativity and Quantum Mechanics and magically just bring them together, the clear consequence of that is- There’s a minimal amount of space. It’s very small (incredibly small). 1.6 x 10–35 meters (The so-called Planck length); So incredibly tiny that if you were to take an individual atom and magnify it to be as large as the observable universe, the planck length under that magnification would grow to roughly be the size of an average tree! So even on atomic scales, the distances being talked about, where the notion of continuity may break down, are fantastically small but it’s not continuous, it’s not infinite…it is discrete, it is pixelated, it is finite. You go beyond this planck length and the energy is so uncertain that it forms black holes. Wait, wait, wait….but black holes do exist…wouldn’t this idea of everything being finite break down at black holes? Did we crack the code? Can we finally find infinity? Are black holes our last light of hope??
WHY DOES EVERYTHING COME DOWN TO BLACK HOLES?
There’s nothing problematic about the black holes themselves. A black hole is a region of spacetime where gravity is so strong that nothing — no particles or even electromagnetic radiation such as light— can escape from it. The problem arises when you go inside it. Einstein’s General Theory of Relativity predicts that if you keep falling in, you’ll eventually reach a point called the singularity; a region which is an infinite curvature in space-time. In a finite time, you’ll reach this point of infinite curvature and infinite density and then just fall out of existence, as if you were never part of the natural world. This is completely catastrophic and violates all of physics.
So what do we do? Just ignore that infinity poses us an existential crisis or…is it trying to tell us something? Well, according to me, this singularity doesn’t happen. The infinity the equations predict is a hint, trying to tell us that there is something new there and general relativity doesn’t work.
Wormholes to the Rescue
Now it really feels like we’re getting into the science fiction stuff! But wormholes existing can save us from our existential crisis. You can have portals that actually go through the black holes. They can open up into an entirely new universe. It’s like saying, “Hey! I have a ball, and within this ball is another ball that holds an area bigger than that of the ball I’m holding.” If you were a microscopic being living at the surface of this ball, you may conclude that the surface is infinite as it would take an infinite amount of time in your imagination of infinity to go from one side of the ball to the other. But as a human, you realize that it’s not infinite. You’re not holding infinity in your hand (Poets would sob reading this).
We talked about infinity being a number and a place but you did read the subtitle of this article right? Is infinity a finite within our minds? It’s finally time to put all pieces of the puzzle together.
The Final Picture
We’re finite creatures. We have access to finite things and we can only do so much in a lifetime. In our final attempt, let’s take a physical system and see what would happen if you just waited for an infinite amount of time.
An Apple a Day Keeps an Infinity Away
Let us take a box (an excellent one). Nothing can come in, nothing can go out. So put an apple in the box and close it. Come back in a month and you’ll find the apple mealy and decayed. Come back in a year and the apple is a real mess. The apple is rotted and bacteria have done their thing. Come back in a 100 years and the apple is probably a kind of dust. Billions and billions of years later, neutrons will decay into protons and other fundamental particles and then it’ll sit there for a very, very long time. The apple will keep changing states.
We do know that these fundamental particles obey the laws of physics. So let’s say the apple is made up of about 10 to the power 20 particles. Then there’s something like 10 to the 10 to the 20 states that the particles can be in. Keep in mind it’s a gigantic number but not infinity. What that means is that if you let the apple sit there for an infinite amount of time, it will go through every possible state it can be in. Eventually, it’ll start having to reuse states it’s already been in. Wait for a long time and at some point, when you open the box…VOILA! There’s your apple again! How can a plasma of fundamental particles at billions of degrees turn into an apple? But eventually it has to. Every possible thing that could exist in the box will exist, and will each exist an infinite amount of times. Why do we care?
Well, we might be in the box :)
In any finite region of space, like the observable universe we now inhabit, there’s a finite amount of energy which is carried by a finite number of particles and those finite number of particles can only be arranged in finitely many distinct patterns. if space does go on infinitely far, the particle pattern has to ultimately repeat. That would mean there would be copies of us out there, an infinite number of copies! Somewhere in the universe, a copy of mine might just come upon this article I published!
Infinity is Forever
If we keep on going along the cosmological timeline, humans, planets, galaxies, black holes, everything will disintegrate. If the universe continues to exist for an infinite amount of time, which physicists think it will, the era of life is just a sliver of time. A 100 billion years of life is nothing compared to infinity. Even if the universe is infinite, there will be a last living creature, there will be a last thought.
The speed of light is the limit and it’s pretty slow. We’d never be able to know whether we have an infinite amount of copies, we’d never be able to know if the universe is infinite. Our finite brains can only have a finite understanding of infinity. You might find all of this daunting. It’ll feel like reading through all of this was a waste. But we have to understand the connectedness behind this. We have to appreciate that we’re a part of the grand picture.
Nothing is permanent in that sense. To my mind, that’s freeing. It frees us from the infinite as a place where value ultimately resides, to a focus on the brief moment we now have. We’re only here for a short time as compared to infinity, and to me that’s a gift that you have of consciousness for the short time that you’re here. The universe lives in the same way that we do. There are things that our mind can’t know but they are real and they exist. Call it the infinite, call it a godly presence, that thing is for real but just not knowable. Can you visualize infinity? Can you visualize a thousand; even that number is too big to imagine.
We’re just like a cat trying to understand quantum mechanics. A cat will never be able to understand quantum mechanics but it will love the feeling of not understanding and it will the love the journey of trying to understand quantum mechanics. We’re finite creatures with finite lives but we do have an infinity hidden within us…an infinity I’d like to call human curiosity. So…
Stay curious!
