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 you 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. And 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 he problem is if you have less than a centimeter of that fiber, it adds another
gram to the tip of you tether. And so now you need a thicker fiber in order to support
that additional force. And 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. And 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. And, 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 which is that
a tether, like anything, is held together by the electromagnetic interaction. That is,
the attractions between all the tiny little charges that makeup 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 cord, 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 or audio books with over 150,000
titles in all areas of literature from fiction to non fiction 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 piggy backing 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 than the 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.