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The speed of light is meant to be the ultimate speed limit in the universe. According to
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Einstein’s special theory of relativity, nothing should move through space faster than
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light. But that doesn’t stop people from trying. Every day I get a lot of messages
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proposing ways to go faster than the speed of light.
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There is the classic method where you shine a laser at the moon. If you can flick that
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beam across the moon’s surface in less than a hundredth of a second, which is not hard
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to do, then that laser spot will actually move across the surface of the moon faster
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than the speed of light. Imagine what that would look like if you were standing on the
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moon. If you were quick enough to perceive it, you would see this laser spot move faster
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than the light coming out of your own laser. How is that even possible?
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Well, in truth, nothing here is really travelling faster than the speed of light. The individual
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particles of light, the photons coming out of my laser are still traveling to the moon
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at the speed of light. It is just that they are landing side by side in such quick succession
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that they form a spot which moves faster than the speed of light. But really it is an illusion,
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nothing is actually going faster than the speed of light. So you couldn’t transmit
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any information this way. Dan asked: What if instead of a laser we used
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a long rigid stick instead? Now surely if you flick your wrist, the tip of this stick
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must move across the surface of the moon, faster than the speed of light.
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Well, unfortunately this won’t work either. As we learned in the slinky drop experiment,
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the fastest a force can propagate through an object is the speed of sound, that is because
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each atom needs to bump into the one next to it to transmit that force. And this is
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a lossy process. So you would be lucky if you any of the energy you have put in at the
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start actually made it to the tip. You would be lucky if the tip moved at all.
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Now this is a really sophisticated idea. Gerard writes: A very special space age engine would
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need to be designed that is capable of doing 10,000 plus rpm in outer space with very high
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torque. Consult Elon Musk for this. As the engine is spinning it slowly deploys two very
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long tethers made from carbon nanotubes on opposing sides. Eventually each carbon nanotube
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tether reaches an amazing length of 285 kilometers. At this point, the end of the tether will
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be traveling at the speed of light. Can you point out some reasons as to why it would
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not work? Yes, Gerard, yes, I can.
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First, any object going in a circle requires a force pulling it in towards the middle of
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that circle. That is called centripetal force. And you can feel it when you whirl a ball
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above your head. Now that force is dependent on the speed of the object squared. So if
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that gets to be too great the tether breaks. Now if you had a single gram rotating at 99
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percent of the speed of light, the amount of force required to pull it towards the center
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would be 300 meganewtons. That is the weight of 6000 fully African elephants. But, you
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are right, carbon nanotubes are tremendously strong. If you had a fiber just eight centimeters
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wide, you could support all of that force.
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But now he problem is if you have less than a centimeter of that fiber, it adds another
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gram to the tip of you tether. And so now you need a thicker fiber in order to support
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that additional force. And that would happen all the way to the base, so the fiber would
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need to get thicker and thicker and thicker all the way back to the motor. And if you
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do the calculation you find that basically 30 meters from the tip the fiber already has
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to be as wide as the observable universe in order to support all of that force. It is
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nuts. But it gets worse. As an object moves faster
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its inertia actually increases. That means it requires more force to accelerate it. In
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fact, that one gram mass going 99 percent the speed of light would require seven times
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the amount of force we calculated before. And so the tether would have to be even thicker.
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But things get even more problematic if you think about speeding up the tip of the tether
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that extra one percent to the speed of light. I mean, since the inertia keeps getting greater
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and greater, it requires more and more force to accelerate it. And, in fact, to speed it
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up that extra little bit to go the speed of light would require an infinite amount of
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energy. Ok, well putting the infinite energy aside,
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let’s say we could create an incredible motor and we could find a material much stronger
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and lighter than carbon nanotube. Is it at least in principle possible that the tip could
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go faster than light? No. There is one final problem which is insurmountable which is that
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a tether, like anything, is held together by the electromagnetic interaction. That is,
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the attractions between all the tiny little charges that makeup the material. Now the
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problem is, electromagnetism is a force carried by photons. I mean, the way that something
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knows that another thing is there to attract it, is by the exchange of photons, these force
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carrying particles. And the problem is the photons themselves move at the speed of light.
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So even if you could create this incredible apparatus with ridiculously strong materials
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and spin it up with infinite energy, it still wouldn’t go the speed of light, because
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the force carrying particles that hold the whole thing together only go the speed of
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light.
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The speed of light really is the ultimate speed limit in the universe.
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Hey, did you see that I made a video about the problem with Facebook over on my second
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channel? It really seems to have struck a cord, so you should check it out if you haven’t
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already. Now I want to thank Audible for supporting
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this episode of Veritasium. They are a leading provider or audio books with over 150,000
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titles in all areas of literature from fiction to non fiction and periodicals. Now this week
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I wanted to recommend the book by Bill Bryson called A Brief History of Nearly Everything.
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When this book first came out I really wanted to dislike it, because I felt like it was
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just piggy backing on Stephen Hawking’s Brief History of Time, but what Bill Bryson
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has done is something truly different and extraordinary. I really think it is a great
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summary and a great sort of investigation of what happens in science. It is a brilliant
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thing to listen to.
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Also, if you go to Audible.com/Veritasium, you can download this book for free, or another
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of your choosing. Now they actually have this book in an abridged form read by Bill Bryson
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himself. It is really interesting to hear the author’s voice. To me he sounds a little
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bit like C. G. P. Gray, but with a hint of a British accent. So you should really check
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that out. Just go to Audible.com/Veritasium.
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All right. Thanks for watching and thanks to Audible for supporting me.
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But there are some things which are going faster than the speed of light, relative to
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us. There are some distant galaxies which are receding at a velocity than the light,
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so we will never be able to see the light that they emit.
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But this doesn’t violate Einstein’s theory of relativity, because they are not moving
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through space faster than light, it is just that the space between us and them is expanding
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so quickly that their effective velocity is greater than the speed of light.