eli5: Why does there need to be 11 additional dimensions for the string theory to work?
In: 5
If you could listen in on string theorists discussion over the years, you’d get something like this:
“Okay, so I think I have this string theory equation written down properly. It’s complicated, but I think it works”.
“But … no, it won’t work the way you have it written, you’re missing a square root there …”
“Aw nuts. Adding the square root would put everything out of whack. *What if* … hear me out … *what if we just say there are FIVE dimensions* instead of four. Then we don’t have to throw in that square root! If we pretend there are five dimensions, the math works!”
“Not quite, chief. Even with five dimensions, you’re missing *n* to the power of infinity, so the math still won’t work.”
“Grrr! You’re right! Adding that would mess things up again. What if we said there were SIX dimensions, then it would work, right?”
[Ten hours later…](https://i.ytimg.com/vi/0r-pvJ3vfIA/maxresdefault.jpg)
“Would you look at that. It finally works. The math finally freakin’ works! And all we had to do was pretend there are ELEVEN dimensions!”
Imagine looking a map of all the flights of airplanes every day (or use Google and just do it). You’d notice all the flights in the Northern Hemisphere bow upwards, towards the North Pole rather than just being a straight line from city to city. Same with the Southern Hemisphere, only dipping towards the South Pole. Why?
If you’re just a lay person looking at this you *can see it’s happening*, you can *describe* the process, but you can’t *justify it*. In fact, if you tried modeling it and predicting it, it would be really hard to do using math. Why?
Because the problem I set up assumes a 2-dimension map, using X and Y coordinates. The *reality* is that the Earth is a sphere and you need a 3-dimension system to really understand what’s happening and suddenly the paths of the planes make sense (google “Great Circles”) and suddenly if you use 3-dimension math to model the paths of the planes the math isn’t even really difficult anymore, it’s actually easy, high-school level calculations. So understanding flight paths is an inherently 3D process, trying to force this down to 2D is both hard and sometimes impossibly complicated.
The point being, you and I are string theory laypeople, we don’t understand *why* string theory does what it does or how to use it but just like going from 2D to 3D makes air travel understandable, going from 4D to whatever-they-say-nowD in String Theory makes the math solvable, it makes it simpler and easier to solve. It also makes *sense* (sort of) of why it does what it does.
So we’re not going *into* string theory saying 17-Dimensions, duhhhh, we’re looking at string theory and *applying* 11 extra dimensions and seeing that it all makes much more sense now and kind of un-complicates itself.
Assuming you know what the hell String theory is in the first place though.
Because the math works out if you put existing data into a higher dimension space.
There is no standard way to interpret why it worked, but if the math works, the interpretation coming after it works as a theory.
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