Over the last hundred years or so, scientists have pushed our understanding of the universe into some extreme conditions, for example the world of the very small, the realm of very high speeds and the under the frigid conditions of near absolute zero. While each of us have developed an intuition about how the world works, it’s very important to remember that this intuition only applies to a very limited set of conditions. For instance, there’s absolutely no reason to expect that matter will act the same in the center of the sun as it does here on Earth on a bright and sunny day.
However, that last statement is hard for some people to accept and, judging by my email inbox, the extreme realm that causes people the most difficulty is what happens when things are going super-fast. In 1905, Albert Einstein published his theory of special relativity. It predicts all sorts of mind-blowing things, for instance distance shorten and clocks slow down.
I made another video about how clocks act at high speed. It turns out that all of those seemingly crazy implications originate from a single cause, or maybe two if we take it slow. So, first, let me tell you what this video isn’t.
It doesn’t tell you about the postulates that Einstein used to build his intuition and it certainly doesn’t derive his equations. Instead, this video tries to tell you the key insights that make it easier to develop a relativistic intuition. I hope to teach you why it is impossible to go faster than the speed of light.
If you’re not a physics groupie, hearing that there is a maximum speed in the universe might surprise you, but it’s true. And, if you are a groupie, you’ve probably heard that the reason that you can’t go faster than light is due to the fact that mass increases when you speed up. It turns out that the explanation of mass changing as you go faster is a wrong one.
I know that statement is going to confuse some people- including those with fairly sophisticated understandings of relativity, but it’s true. However, that then leaves an open question. Just why is it that you can’t go faster than the speed of light?
It turns out to be due to a combination of a deep and fundamental property of the universe and fairly simple geometry. So, let me explain how that all works. The first of the two crucial insights is that Einstein taught us that space and time were not separate entities, but rather they are two components of a bigger idea, called spacetime.
I’ll give you a helpful visual way to think of this in a moment, but for right now, just trust me on this. Then we need to combine that insight with the observation that everybody sees the speed of light to be the same, no matter how fast they are moving with respect to one another. Let’s start with an analogy and then come back to relativity.
To understand the analogy, you need to imagine a car driving on a huge flat surface. Further, you need to imagine that the car can only move at one speed, say 60 miles per hour. Or, so the comments don’t fill up with metric-snobbery hate mail, 100 kilometers per hour.
Now let’s put a couple arrows on the screen to point out north and east. While we know the overall speed the car is going, we don’t know how much of it is in the east direction and how much of it is in the north direction. So let’s take a closer look at that.
The car can move entirely in the eastward direction, which means that it has no motion in the northward direction. Or, the car can move entirely northward and not at all eastward. Or we can live dangerously and move towards the northeast.
In this case, we see that the car is moving in both the east and north directions, with neither direction getting all of the motion. So that’s the core analogy and hopefully it’s very clear. Now, let’s bring in relativity.
In relativity, we don’t have the east and north directions. Instead, we have spacetime. Let’s imagine that the horizontal direction is space and the vertical direction is time.
So suppose that there is a single and fixed speed that we can travel through spacetime. This happens to be true, so it’s not a ridiculous supposition. We can therefore mix these ideas with our earlier analogy.
An object can move vertically. In that case, they are not moving through space and they're moving entirely through time. That’s probably what you’re doing right now.
You’re sitting and watching this video, so your position in space isn’t changing. However, you are experiencing time. You aren’t moving through space, but you're moving through time.
On the other hand, what happens as you start moving through space? That’s a fancy way to say that you gain some velocity. Well we see here that what starts to happen is that as you begin to move through space, you move less through time.
And eventually, when you move only through space, you don’t move through time at all. And this is basically what relativity says. As you move faster and faster, your clocks slow down.
And, as you get very close to the speed of light, your clocks very nearly stop. We’ve scientifically proven that this is what happens and I direct you to my video on time dilation so you can see one way that we’ve tested that. So, this brings us to our fundamental realization of relativity.
The reason that we can’t move through space faster than the speed of light is because we are constantly moving through spacetime at a single speed- the speed of light. If we aren’t moving through space, we experience time in the fastest way; and if we start moving through space, we experience time slower and slower. Finally, since we're moving through spacetime at a single speed, that means that when we're moving only through space, there is no more speed to gain.
We move through space at the speed of light and that’s it. This observation wasn’t made by Einstein. It was made by his mentor, Herman Minkowski.
Minkowski was one of Einstein’s mentors and he was a better mathematician. Two years after Einstein’s seminal 1905 paper, Minkowski appreciated the geometrical underpinnings of special relativity and had determined this deep and fundamental explanation why we can’t travel faster than light through space. There are two final important points.
First, while Minkowski showed why light speed is the maximum speed through space, what he didn't explain was why we move only at one speed through spacetime. To this day, nobody really knows. It seems to be a fundamental property of spacetime.
Maybe it will take another person as smart as Einstein to figure out that particular conundrum. The second point is more technical and I mention it only for the real physics nerds. In my analogy, I connected space and time as being similar to east and north and there is a lot of merit in that.
Morphing from motion through time to motion through space was like turning a car from moving north to moving east. However, this analogy is also technically inaccurate. From a mathematical point of view, it uses the geometry of circles, while the proper geometry is that of hyperbolas.
I only bring this up because I want you to know my analogy is imperfect and you shouldn’t push it too far. Otherwise you might come to a numerically incorrect conclusion and think that you’ve made a new discovery. If you want to dig into this more deeply, be sure to use the full and proper Minkowski mathematics.
Still, even with the limitations I’ve mentioned, the core point is valid. The reason that you can’t move faster through space than the speed of light is because that every object moves through spacetime at one and only one speed- the speed of light. Once you’ve embraced that central idea and the fact that space and time are just like two directions of spacetime, then all of those seemingly weird observations of relativity just click into place and special relativity makes total sense.
So I don't know about you, but I think this insight about relativity is just about the coolest thing ever. If you liked this video, be sure to like, subscribe, and share- let's get those numbers up. And let me know what you think in the comments.
I'll see you next time, and keep on physics-ing.
