I've been trying to figure out why things stop around you when you're going at the speed of light, rather than going incredibly slowly. And I would like to know what that ratio is.

It's the Lorentz factor.

 

Specifically, if you are moving at the speed of light (not possible), no time passes for you, so everything moves infinitely fast.

Aight, though I'd still like to know the ratio of: Time slows down X much for you, when you speed up Y much.

t'=ty, y is Lorentz factor

I've been trying to figure out why things stop around you when you're going at the speed of light, rather than going incredibly slowly. And I would like to know what that ratio is.

 

A few things

 

1. You cannot cannot go at the speed of light. Nothing with any mass can go at the speed of light.

2. We have no physics which tells us what world around us would look like when we go the speed of light because 1.

3. We use Special Relativity to calculate and predict what the world around us looks like when we go close to the speed of light.

4. If you look at a moving clock (you are at rest as far as you are concerned) then each tick of the clock will take longer.

5. If you look at a moving ruler ( you are at rest as far as you are concerned) then the ruler will be contracted/shorter.

6. You cannot extrapolate from Special Relativity (which deals only with massive objects at speeds less than the speed of light) to a new scenario where something massless (even a photon) is moving at the speed of light - that would require new physics.

 

In short the answer to "what happens when you go at the speed of light ?" is that we don't know because we are pretty sure it is impossible.

[latex]\Delta t'= \Delta t \cdot \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/latex]

 

If you look at the bottom of the fraction - v is relative velocity and c is the speed of light. v is always less than c, so the bottom of the fraction is always less than one, so the tick in the moving frame (Delta t') is always longer than the tick in your stationary frame (Delta t)