Will This Go Faster Than Light?

The speed of light is meant to be the ultimate speed limit in the universe. According to Einstein’s special theory of relativity, nothing should move through space faster than light. But that doesn’t stop people from trying.

Every day I get a lot of messages proposing ways to go faster than the speed of light. There is the classic method where you shine a laser at the moon. If you can flick that beam across the moon’s surface in less than a hundredth of a second, which is not hard to do, then that laser spot will actually move across the surface of the moon faster than the speed of light. Imagine what that would look like if you were standing on the moon.

If you were quick enough to perceive it, you would see this laser spot move faster than the light coming out of your own laser. How is that even possible? Well, in truth, nothing here is really travelling faster than the speed of light. The individual particles of light, the photons coming out of my laser are still traveling to the moon at the speed of light. It is just that they are landing side by side in such quick succession that they form a spot which moves faster than the speed of light.

But really it is an illusion; nothing is actually going faster than the speed of light. So you couldn’t transmit any information this way.

Dan asked: "What if instead of a laser we used a long rigid stick instead? Now surely if you flick your wrist, the tip of this stick must move across the surface of the moon, faster than the speed of light." Well, unfortunately, this won’t work either.

As we learned in the slinky drop experiment, the fastest a force can propagate through an object is the speed of sound. That is because each atom needs to bump into the one next to it to transmit that force. And this is a lossy process. So you would be lucky if any of the energy you have put in at the start actually made it to the tip. You would be lucky if the tip moved at all.

Now this is a really sophisticated idea. Gerard writes: "A very special space age engine would need to be designed that is capable of doing 10,000 plus rpm in outer space with very high torque. Consult Elon Musk for this." As the engine is spinning, it slowly deploys two very long tethers made from carbon nanotubes on opposing sides. Eventually, each carbon nanotube tether reaches an amazing length of 285 kilometers. At this point, the end of the tether will be traveling at the speed of light.

Can you point out some reasons as to why it would not work? Yes, Gerard, yes, I can. First, any object going in a circle requires a force pulling it in towards the middle of that circle. That is called centripetal force. You can feel it when you whirl a ball above your head.

Now that force is dependent on the speed of the object squared. So if that gets to be too great, the tether breaks. Now, if you had a single gram rotating at 99 percent of the speed of light, the amount of force required to pull it towards the center would be 300 meganewtons. That is the weight of 6000 fully African elephants.

But, you are right, carbon nanotubes are tremendously strong. If you had a fiber just eight centimeters wide, you could support all of that force. But now the problem is if you have less than a centimeter of that fiber, it adds another gram to the tip of your tether. So now you need a thicker fiber in order to support that additional force. That would happen all the way to the base, so the fiber would need to get thicker and thicker and thicker all the way back to the motor.

If you do the calculation, you find that basically 30 meters from the tip, the fiber already has to be as wide as the observable universe in order to support all of that force. It is nuts. But it gets worse. As an object moves faster, its inertia actually increases. That means it requires more force to accelerate it.

In fact, that one gram mass going 99 percent the speed of light would require seven times the amount of force we calculated before. And so the tether would have to be even thicker. But things get even more problematic if you think about speeding up the tip of the tether that extra one percent to the speed of light.

I mean, since the inertia keeps getting greater and greater, it requires more and more force to accelerate it. In fact, to speed it up that extra little bit to go the speed of light would require an infinite amount of energy. Ok, well putting the infinite energy aside, let’s say we could create an incredible motor and we could find a material much stronger and lighter than carbon nanotube.

Is it at least in principle possible that the tip could go faster than light? No. There is one final problem which is insurmountable— a tether, like anything, is held together by the electromagnetic interaction. That is, the attractions between all the tiny little charges that make up the material.

Now, the problem is electromagnetism is a force carried by photons. I mean, the way that something knows that another thing is there to attract it, is by the exchange of photons, these force-carrying particles. And the problem is the photons themselves move at the speed of light.

So even if you could create this incredible apparatus with ridiculously strong materials and spin it up with infinite energy, it still wouldn’t go the speed of light because the force carrying particles that hold the whole thing together only go the speed of light. The speed of light really is the ultimate speed limit in the universe.

Hey, did you see that I made a video about the problem with Facebook over on my second channel? It really seems to have struck a chord, so you should check it out if you haven’t already. Now I want to thank Audible for supporting this episode of Veritasium.

They are a leading provider of audio books with over 150,000 titles in all areas of literature from fiction to nonfiction and periodicals. Now this week I wanted to recommend the book by Bill Bryson called A Brief History of Nearly Everything. When this book first came out, I really wanted to dislike it because I felt like it was just piggybacking on Stephen Hawking’s Brief History of Time, but what Bill Bryson has done is something truly different and extraordinary.

I really think it is a great summary and a great sort of investigation of what happens in science. It is a brilliant thing to listen to. Also, if you go to Audible.com/Veritasium, you can download this book for free, or another of your choosing.

Now they actually have this book in an abridged form read by Bill Bryson himself. It is really interesting to hear the author’s voice. To me, he sounds a little bit like C. G. P. Gray, but with a hint of a British accent. So you should really check that out. Just go to Audible.com/Veritasium.

All right. Thanks for watching and thanks to Audible for supporting me. But there are some things which are going faster than the speed of light, relative to us. There are some distant galaxies which are receding at a velocity greater than light, so we will never be able to see the light that they emit.

But this doesn’t violate Einstein’s theory of relativity because they are not moving through space faster than light; it is just that the space between us and them is expanding so quickly that their effective velocity is greater than the speed of light.