Light Speed

Light

299 792 458 m/s (according to google.)

It looks like we've reached light speed.

But we haven't. Our line can get infinitely close to light speed but it'll never reach it. The reason for that is a little tricky to grasp, so let me make an analogy for it. You know the number π right? It's 3.14... well: that's our answer! Not the number itself, but look at the next card.

Why we can't reach it.

If the speed of light is 3.15 m/s, and we're traveling at 3.14 m/s, we can still increase our speed. But nature won't let us accelerate very fast anymore, since if we would be actually travelling at this proportion of the speed of light, we would be traveling REALLY fast. That would be 99.7% the speed of light, which I remind you is 299 720 458 m/s! Anyways, back to my point. We can now only accelerate very slowly. Let's do this.

You all know what a v-t graph is, right?

In case you don't, it's a 2D graph in which the y axis is velocity and the x axis is time. The area under the curve is the distance traveled. The curved line itself represents the acceleration.

To finish.

Just so you don't get confused, I remind you that we have been using a fictional speed for light. Light's real speed is 299 792 458 m/s, not 3.15 m/s. Also, keep in mind that as of today and probably decades to come, we don't and won't have the technology to travel anywhere near the speed of light.

Let's do this.

Our velocity changes from 3.14 m/s to 3.141 m/s. Again. 3.1415 m/s. Again. 1.14159 m/s. This goes on for a while. We are accelerating, but we never will reach the speed of light, 3.15 m/s. We're stuck at our limit for meters, decimeters, centimeters and millimeters per second. We can still increase our micrometers, then our nanometers, and so on. But we'll never reach the speed of light, 3.15 m/s.

Let's look at my graph for infinitely increasing acceleration.

Sorry, I drew this on an iPad, so the lines aren't perfect. By the way, the vertical line on the right represents the speed of light. It should be just a point, but I made it a line for a better perspective.

As the line progresses towards the right...

You can see the velocity (Y axis) increasing while the time (X axis) is decreasing. This means that the object travelling is achieving more velocity increase in smaller amounts of time, and ever greater distances.

π < 3.15 for instance.

π is 3.1415926535897932... Let's change the speed of light for a moment, but let's also keep it's properties. Now, the speed of light is 3.15 m/s. We're traveling at 3.14 m/s. I know, that's a little too slow, but it still works well for this example. Next slide.