How Many Dimensions Are There?

How Many Dimensions Are There?

How Many Dimensions Are There?

The question of how many dimensions exist is a tricky one. Many of you probably expect to find a concrete answer, but if you put two physicists together, they might not even agree on how many there are. Depending on the theory you subscribe to, the number can go up to 26.

But let’s start with what you can perceive (and maybe conceptualize). As humans, we perceive in 3 dimensions; length, width, and depth. Most of us can grasp the idea of a 4th dimension, time. Einstein’s Theory of General Relativity operates within these four dimensions, but this is where Einstein’s theory also stops adding dimensions.

To completely oversimplify, general relativity gave us the idea that gravity is tied to time and space. It asks you to imagine space and time (literally referred to as spacetime) as a large cloth. When you set a massive object into spacetime, like a black hole, the cloth is distorted. For those of you who have seen Interstellar, the concept of losing a large sum of years after spending a relatively short period of time near a black hole due to its mass comes in part from Einstein (ergo, an object of such great mass warps space and time itself). We don’t recommend flying near black holes for a lot of reasons, but getting your atoms torn apart is probably chief among them.

Einstein’s theory may have operated within four dimensions, but how then, do we get to 26?

What Is a Dimension?

Before we go on, it’s probably important to define what exactly a dimension is. There are the dimensions we can perceive and attempt to conceptualize, and that’s what we’re talking about now. But we should establish that mathematically, a dimension is simply another coordinate on a plane.

Hopefully you still remember some middle/high school geometry, specifically the x – y coordinate plane. This is a mathematical representation of 2 dimensions. You also might remember that to graph a circle on a 2 axis plane, the equation is x2 + y2 = 1.

Mathematically speaking, you could continue to add as many dimensions as you wanted, x2 + y2 + z2 = 1 and so on to your heart’s desire. But, while you technically could go on forever, those of you following along probably have figured out that the human mind can’t conceptualize this shape past the third axis. x2 + y2 + z2 = 1 made sense since it turned the circle into a sphere, but x2 + y2 + z2 + a2 = 1 doesn’t compute with how we interact with the world. It’s important to recognize that you could symbolically add as many dimensions as you wanted, though.

Are There More Than Four Dimensions?

You’re probably still wondering what dimensions past four represent, and it’s a lot to take in because they might be different depending on where you’re looking. Let’s start with the origins of the 5th dimension as a concept. Theodor Kaluza came in, and under the principles outlined above (that you could continue to add dimensions to Euclidean geometry forever), threw the idea of a 5th dimension into the mix. It turns out applying that idea to Einstein’s theory of general relativity checked out mathwise, but the idea wasn’t received too well when it was presented in 1919.

Fast forward to the 60’s and the advent of String Theory. That’s when we started smashing things together and discovered elementary particles (we also started looking at strong/weak nuclear forces). This lead to all sorts of funky stuff, where observing something changes its properties (Heisenberg Uncertainty Principle).

Long story short, we ended up with 10 total dimensions. We have the four dimensions established by Einstein (these are the the big ones we consider), and added six more (“micro-dimensions”). One of the six is dedicated to electromagnetic forces, while the other five exist for nuclear forces. 

Can We Go Beyond 10 Dimensions?

Things start to get even cloudier beyond 10 dimensions. We saw the advent of M-Theory in the 90’s, and before you ask, no, we don’t know what the M stands for. The guy who made it (Edward Witten) thinks it should be “magic” or “mystery,” while ceding that an actual word should be chosen only when M-Theory gets off the ground more and has its fundamentals laid out. This one adds an 11th dimension through work on supergravity and supersymmetry.

This tends to be where things stop, as even diehard String Theorists are going to tell you it’s already extremely difficult to prove 10 or even 11 dimensions. But, there is a possibility that there exists dimensions up to 26. It’s a little much to distill for today, but if you’re interested in intense Bosonic String Theory (looking at the Higgs Boson over here), here’s some stuff out of Cornell on it.

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