| Transcript |
| 0:00 | · | I believe there's intelligent life on other planets. And the most plausible |
| 0:04 | · | reason why they haven't contacted us is that we're too boring. I mean, |
| 0:08 | · | we haven't even figured out how to send information faster than light. Pathetic. |
| 0:13 | · | But wait, let me guess. You've heard that it's impossible to |
| 0:17 | · | send information faster than the speed of light because, er, physics. Yes, |
| 0:22 | · | I've heard that too. But I think it's wrong. And in this video, I want to explain why. |
| 0:28 | · | Is it possible to break the speed of light limit? That's what we'll talk about today. |
| 0:37 | · | If you've been following this channel for a really long time, first of all, thank you, |
| 0:42 | · | I know it isn't always easy. Second, you may remember that I made a video |
| 0:48 | · | about faster than light travel already a few years ago. But I think no one understood it. |
| 0:53 | · | In fact, when I watched it again recently, I didn't understand it either. |
| 0:58 | · | So please give me a second chance. Because I think it's becoming increasingly relevant to get this |
| 1:04 | · | right. And this time, I'll try to do it better. I'll even let you leave the toilet seat up. |
| 1:10 | · | In the past year or so, there's been a lot of talk about unexplained aerial phenomena, |
| 1:15 | · | formerly known as UFOs. I don't actually believe any of those are of extra-terrestrial |
| 1:21 | · | origin because, as I said, we're just too boring for aliens to bother visiting us. |
| 1:26 | · | Then again, what do I know? Maybe some of those aerial phenomena really are space probes from |
| 1:34 | · | alien species. And if we want to properly evaluate how likely that is, we need to talk |
| 1:40 | · | about the possibility of travelling faster than light, or at least sending information |
| 1:44 | · | faster than light. Because if it's possible at all, then that's what the aliens are doing. |
| · | The Speed of Light as Limit |
| 1:51 | · | The idea that the speed of light is a limit comes from Albert Einstein's theory of Special |
| 1:56 | · | Relativity. Yes, this guy again. The speed of light plays a special role in his theory |
| 2:02 | · | because it's the only speed that's the same for all observers. And just to make sure, |
| 2:08 | · | I mean the speed of light in vacuum. The speed of light in a medium, any medium, |
| 2:13 | · | is slower than the speed of light in vacuum, |
| 2:16 | · | and depends on how you move relative to the medium. But the speed of light *in vacuum |
| 2:22 | · | does *not depend on how fast you move because there's nothing for you to move relative to. |
| 2:28 | · | I know this sounds about as exciting as flossing teeth, but it has some unexpected consequences, |
| 2:34 | · | and I don't mean that your crowns pop off. Suppose you and your friend, let's call him Bob, |
| 2:39 | · | both have a water hose, and it spits out water at, say 10 kilometres per hour. Bob |
| 2:45 | · | gets on a train which moves at 200 kilometres per hour. If you live in the United States, |
| 2:50 | · | make that 20, then he turns on his water hose again. The water moves |
| 2:55 | · | with 10 kilometres per hour relative to him. But how fast does it move relative |
| 3:01 | · | to you? You'd expect it to be the speed of the water plus the speed of the train, right? |
| 3:07 | · | Now imagine you don't have water hoses but laser pointers. They send out light with, |
| 3:12 | · | well, the speed of light. Your friend Bob gets on a train again. In vacuum, |
| 3:17 | · | of course. Because this is theoretical physics, where people don't breathe, |
| 3:21 | · | cows are spheres, and 3 is either equal to pi or infinity, depending on whom you ask. |
| 3:27 | · | How fast do you see the light of Bob's laser? You'd expect this to be faster than the light |
| 3:33 | · | that comes out of your laser pointer by the speed of the train, but not so. It moves with |
| 3:39 | · | the exact same speed as yours. Because the speed of light is always the same. |
| 3:44 | · | This is what was confirmed with the famous Michaelson-Morley experiment, |
| 3:48 | · | and it has a very odd consequence: You can't catch up with light. It doesn't matter how |
| 3:55 | · | fast the train is, light will still move away from it with the speed of light. |
| 4:00 | · | If that didn't make your crowns pop off you've probably heard it so many times |
| 4:04 | · | before that you've forgotten how remarkable it is. That, or you have a very good dentist. |
| 4:09 | · | We can quantify the difficulty of catching up with light by asking how much energy it |
| 4:15 | · | takes to accelerate an object. Let's suppose the object has a mass m. This |
| 4:21 | · | mass corresponds to an energy which is given by the most famous equation ever, |
| 4:25 | · | E equals m c square, where E is the energy and c is the speed of light. |
| 4:29 | · | But now we accelerate this massive object from zero velocity to some other velocity, |
| 4:35 | · | v. The energy you need for this acceleration is the total energy of the object at the new |
| 4:42 | · | velocity, minus the energy it previously had. In Einstein's theory, the total energy of an |
| 4:48 | · | object that moves relative to you with velocity v is given by this expression. |
| 4:53 | · | Now if you want to know the kinetic energy, |
| 4:55 | · | you take this and subtract the same expression for zero velocity. |
| 5:00 | · | So you get this somewhat messy expression, but don't despair, it isn't as bad as it looks. |
| 5:06 | · | For one thing, when the velocity, v, is much smaller than the speed of light, |
| 5:10 | · | then the ratio v over c is much smaller than one. In this case, the complicated thing with |
| 5:16 | · | the square root is approximately one plus one half v over c square, the one cancels out and the c's |
| 5:23 | · | cancel out and you get one half m v square, which you might remember is just the kinetic energy. |
| 5:29 | · | But we're more interested in the case where the velocity gets close to the speed of light, |
| 5:35 | · | so v over c gets close to 1. Then this factor gets close to zero, |
| 5:41 | · | and the entire energy gets close to one over zero, which is infinity. |
| 5:45 | · | This means if you want to accelerate an object until it reaches the speed of light, |
| 5:50 | · | you need an infinite amount of energy. Another way to put this is that the only way you can move |
| 5:56 | · | at the speed of light is when your mass is zero. Even a keto diet isn't going to do that for you. |
| 6:03 | · | This is where the idea comes from that the speed of light is a limit that you can't cross. |
| 6:09 | · | But… this argument has some issues. The first issue is that it doesn't mean faster |
| · | The Speed of Light as Barrier |
| 6:16 | · | than light travel is forbidden in Einstein's theory. Indeed, his theory is entirely compatible |
| 6:22 | · | with faster-than-light travel. The problem seems to be instead that you can't accelerate |
| 6:27 | · | from below the speed of light to above the speed of light. It's more like a barrier than a limit. |
| 6:33 | · | The second issue is more a peculiarity. It's that on all other occasions when physicists |
| 6:40 | · | see some quantity go to infinity, they'll tell you that infinity is unphysical and a sign that |
| 6:45 | · | the maths doesn't properly work. Big bang, black holes, non-renormalizable effective field theory, |
| 6:51 | · | whatever. If there's a singularity, they'll say it's a mathematical artefact |
| 6:56 | · | and not real. They don't say that in this case, and I think they should. |
| 7:01 | · | The third issue is that we have a counterexample to the claim that one needs an infinite amount |
| 7:06 | · | of energy to reach the speed of light, which makes the argument extremely suspect. |
| 7:12 | · | But to see why I say this, I first need to tell you where mass comes from. No, |
| 7:18 | · | it's not too much cheese, it's simpler than that. |
| 7:20 | · | Most of the mass of objects around you isn't really mass, it's binding energy. You see, |
| 7:27 | · | almost the entire mass of atoms is in the nucleus. The nucleus is made of neutrons and protons, |
| 7:33 | · | and the neutrons and protons are each made of three quarks. For the neutron |
| 7:38 | · | that's two down and one up, and for the proton it's two up and one down. Quarks, |
| 7:44 | · | not thumbs, I mean. The quarks do have masses, but if you add them together, |
| 7:48 | · | the sum is far less than the mass of either the neutron or proton. |
| 7:53 | · | Instead, most of the mass of neutrons and protons is the binding energy from the strong nuclear |
| 7:59 | · | force that holds them together. We *interpret it as mass because E equals m c square. But |
| 8:06 | · | this means it's really odd to put the mass of an object into this equation in Einstein's formula. |
| 8:12 | · | Because really if you look at the object microscopically, most of it isn't mass. And, |
| 8:18 | · | yes, that means most of you isn't mass either. You're almost entirely made of pure energy. |
| 8:23 | · | Though when I see how much time you spend watching YouTube I find that hard to believe. |
| 8:28 | · | What's with the remaining mass, the part that isn't binding energy? Electrons and quarks |
| 8:35 | · | do have masses, albeit very small ones. These masses come from the Higgs-field, |
| 8:40 | · | not to be confused with the Higgs-boson. To be more precise, the masses come from the condensed |
| 8:46 | · | Higgs field. This Higgs-field condensate fills the entire universe and drags on |
| 8:52 | · | particles. It's kind of like the 19th century aether, but with two important differences. |
| 8:58 | · | First, the aether was believed to be necessary for light to travel. But for the Higgs-field |
| 9:04 | · | it's the opposite. The particles of light, the photons, are massless, which means they |
| 9:09 | · | don't feel the Higgs field at all. But other particles do feel it. When the field condenses, |
| 9:15 | · | it sticks to the particles. That slows them down and it looks to us like they have a mass. |
| 9:21 | · | Another difference between the condensed Higgs-field and the aether is that the |
| 9:26 | · | Higgs-condensate looks the same for everyone, regardless of how fast they move. It's just a |
| 9:33 | · | number at each point in space-time and everyone agrees on what this number is. It's like the |
| 9:38 | · | number of socks in your washing machine. Doesn't matter how fast the spin cycle is, |
| 9:43 | · | the number of socks doesn't change. Or if it does, I guess it's time for new socks. |
| 9:48 | · | The aether on the other hand was believed to be basically like a fluid. Some people would |
| 9:53 | · | drift with the flow, and some people would move against it, and they'd see different things. |
| 9:59 | · | This is *not the case for the Higgs-field and its condensate. If you like technical terms, |
| 10:05 | · | and I just know you do, it's a Lorentz-scalar and invariant under Poincare transformations. |
| 10:10 | · | Ok, so the masses of fundamental particles come from the Higgs-field. But. This is |
| 10:17 | · | only the case when the field is condensed and that wasn't the case in the early universe. |
| 10:23 | · | Think of an early morning in spring. No, not the coffee, I mean the dew on the grass. Where does it |
| 10:29 | · | come from? Well, air contains water vapour, which means that individual water molecules float around |
| 10:36 | · | in the air. But warm air can hold more water vapour than cold air. If the air temperature |
| 10:42 | · | drops during the night, the water molecules collect to form drops which are too heavy |
| 10:47 | · | to keep floating, and they fall to the ground. The Higgs field has done a very similar thing, |
| 10:52 | · | not at night, but in the early universe. In the early universe it was really hot. There |
| 10:59 | · | was a Higgs-field but it wasn't condensed, kind of like the water vapour in the air. |
| 11:04 | · | But then the temperature dropped, and the Higgs field condensed. This condensate now fills the |
| 11:11 | · | entire universe. But it was only when the Higgs field condensed that particles acquired masses. |
| 11:18 | · | It's a phase transition called “electroweak symmetry breaking” and it's believed to have |
| 11:23 | · | happened about 10 to the minus 11 seconds after the Big Bang at |
| 11:28 | · | a temperature of 10 to the 15 Kelvin, that's much hotter than even the centre of the sun. |
| 11:33 | · | What all this means is that in the early universe none of the particles had masses. |
| 11:39 | · | They were all massless, and they were all moving with the speed of light. Later they were not. And |
| 11:45 | · | here's the important bit: The energy that was released in this phase transition was finite. |
| 11:51 | · | If it hadn't been, we wouldn't be here, and someone would have written a paper about that, |
| 11:56 | · | I'm sure. But the equation that we looked at earlier said that the difference in energy |
| 12:01 | · | should have been infinite. What gives? Mathematically it's pretty obvious what |
| 12:08 | · | goes wrong with the earlier argument. If you look at this equation again, you see that if |
| 12:13 | · | this factor goes to zero, but the mass *also goes to zero, then the ratio can well remain finite. |
| 12:21 | · | This doesn't help us at all to travel at the speed of light. Because we can't just |
| 12:26 | · | uncondense the Higgs field. Even if we could, it'd basically evaporate the traveller and, I mean, |
| 12:32 | · | I'm not a doctor, but that's probably not healthy. So, this isn't going to let us build a warp drive. |
| 12:38 | · | But it shows that the argument that the speed of light is a barrier isn't even technically correct. |
| · | Time Travel Paradoxes |
| 12:44 | · | There is another reason that physicists often bring up for why you can't travel |
| 12:49 | · | faster than the speed of light, which is that it can allegedly cause time-travel paradoxes. |
| 12:54 | · | The argument goes like this. Suppose Alice observes a spaceship which goes |
| 13:00 | · | by faster than the speed of light. Zoom there it goes. Her friend Bob |
| 13:05 | · | can't afford the new super-duper spaceship and lamely zooms by in last year's model, |
| 13:10 | · | at merely 90 percent the speed of light. Then Bob would see the space-ship going back in time. |
| 13:16 | · | Let's draw this into a space-time diagram to see why. The horizontal axis depicts one direction |
| 13:22 | · | of space, so left and right, for example. And the vertical axis is time. A spaceship which |
| 13:29 | · | doesn't move, according to this axis, just makes a vertical line. A spaceship at constant velocity is |
| 13:36 | · | a line which moves at some angle. By convention a 45-degree angle is the speed of light. |
| 13:43 | · | Alice just sits there and moves on this straight line. And everything |
| 13:47 | · | that happens on a perfectly horizontal line happens simultaneously, according to Alice. |
| 13:54 | · | The faster-than-light space-ship goes by like this. And Bob moves on this line. The question |
| 14:00 | · | is now what Bob sees. For this, let's look at two particular events. And let's make sure those |
| 14:06 | · | events have a clear arrow of time from entropy increase, let's say someone drops a raw egg. The |
| 14:13 | · | guy in the spaceship stumbles here, and the egg smashes to the ground here. This means, |
| 14:19 | · | importantly, that time on the space-ship passes in this direction, and *not in the other direction. |
| 14:25 | · | Since Bob is moving relative to Alice, he sees different events happen simultaneously. |
| 14:31 | · | I explained this previously in my video on why the past still exists. So, well, |
| 14:36 | · | either take my word for it or watch the other video. |
| 14:39 | · | For Bob, events that happen at equal times are on these straight lines, not on horizontal lines. You |
| 14:48 | · | can then see that for Bob the order of events is that the egg first smashes to the ground and then |
| 14:54 | · | gets dropped. It seems that for Bob the time order of the faster than light ship is reversed, crazy! |
| 15:02 | · | The first reaction you may have to this is: Who cares what Bob sees? I mean you can watch |
| 15:07 | · | this video in reverse and that doesn't mean I actually spoke in reverse. Fair enough. |
| 15:13 | · | The second reaction is to point out that this isn't what either Alice or Bob see anyway. You |
| 15:19 | · | can't see a faster than light ship coming for the same reason you can't hear a supersonic |
| 15:24 | · | plane coming. What do you want to see it with? Instead, both Alice and Bob will only see the |
| 15:30 | · | spaceship after it's gone by and then they'll see it moving away in both directions. And again, |
| 15:36 | · | you can say, so what? I mean gravitational lensing distorts galaxies into rings, alright, |
| 15:42 | · | but that doesn't mean the galaxy is a ring. It's just some weird trick on our perception. |
| 15:47 | · | And that's entirely correct… But, you know, physicists have noticed that too. Thing is, |
| 15:53 | · | this wasn't the entire argument. There's a piece missing which goes like this. |
| 15:58 | · | Imagine you are Bob, and there's really a spaceship that can go faster than light and |
| 16:04 | · | according to you that goes back in time. Let's not ask what this means but what you can do with it. |
| 16:10 | · | If the time on the spaceship really goes forward this way, then you can |
| 16:16 | · | give a message to the guys as they come by. They take your message to Andromeda, hand it |
| 16:21 | · | over to another faster-than light spaceship, and the second ship brings the message back to |
| 16:27 | · | you. It would then arrive before you sent it. This means you could send messages to yourself |
| 16:34 | · | back in time, and *that causes a lot of trouble. Imagine that this video greatly |
| 16:39 | · | disturbs you and you send a message to your younger self to not watch it, |
| 16:44 | · | then you'd never have sent the message in the first place, so did you, or didn't you watch it? |
| 16:50 | · | This type of construction is also called a time-like closed loop, it's a loop in time. |
| 16:56 | · | The argument then concludes that if faster-than-light travel was possible, |
| 17:01 | · | that would lead to causality paradoxes, so it must be impossible. |
| 17:06 | · | But this argument is also wrong. The reason is that just because according to Bob there's |
| 17:12 | · | a spaceship going that way with a time that goes forward on the space-ship in |
| 17:18 | · | a direction that Bob calls backwards in time, that doesn't mean if a space-ship goes that way |
| 17:24 | · | then its internal forward-in time direction would be that way. If the time-direction on |
| 17:29 | · | the ship goes that way, they can't deliver a message to your younger self. Instead, |
| 17:34 | · | your younger self can send a message there, and nothing's weird about that. |
| 17:39 | · | Physicists do have a reason to assume that time on the space-ship could go this way, |
| 17:45 | · | but it's not a good reason. It's because in special relativity all observers must be treated |
| 17:51 | · | the same. In Special Relativity, if you think that this is possible, then this must also be possible. |
| 17:58 | · | But Special Relativity is special because it doesn't contain gravity and this means |
| 18:04 | · | it doesn't actually describe reality. For this, we need general relativity. And while the time-travel |
| 18:11 | · | argument is correct in special relativity, it is not correct in general relativity. |
| 18:15 | · | I know this video is some tough going so let's stop for a moment to appreciate where |
| 18:21 | · | we are. I summarised the usual argument for why faster than light travel leads to |
| 18:27 | · | time-travel paradoxes. I'm about to explain why this argument doesn't apply in the real universe. |
| 18:34 | · | The usual argument uses special relativity according to which only relative velocities |
| 18:40 | · | are physically relevant. In special relativity, you can't be at a velocity of absolute zero, |
| 18:45 | · | that just makes no sense. But the real universe contains stuff, as |
| 18:50 | · | you've probably noticed. You can take all this stuff, calculate the average velocity that it |
| 18:56 | · | moves with. And then you can define absolute rest to be motion that has no relative velocity |
| 19:01 | · | to the average of all that stuff. Since you like technical terms so much, it's called the |
| 19:07 | · | “co-moving frame”. It's the reference frame that moves along with matter in the universe. |
| 19:13 | · | We are currently not at rest relative to the average of stuff in the universe because the |
| 19:19 | · | earth goes around the sun and the sun goes around the centre of the milky way and the |
| 19:24 | · | milky way is rushing towards something called the big attractor that no one |
| 19:28 | · | really knows what it is. If you wanted to be at rest with the universe you'd have |
| 19:33 | · | to run at 300 kilometres per second into this direction. No, wait. This. Or, this? |
| 19:42 | · | Alright, so there's matter in the universe that moves one way and not another. But what does this |
| 19:48 | · | have to do with the time-travel story? Suppose you are Alice again but now you are Alice in a |
| 19:54 | · | universe with general relativity and you are moving with the stuff, you are in the |
| 19:59 | · | co-moving frame. And now assume that faster than light travel is only allowed forward in |
| 20:05 | · | time in this particular frame. In this case you can't make loops in time, regardless of what |
| 20:11 | · | Bob thinks he sees. The co-moving frame defines one direction as forward in time. The only thing |
| 20:17 | · | Bob can do is send two signals to Andromeda, and there's nothing Paradoxical about that. |
| 20:22 | · | You may wonder now what the motion of matter should have to do with the possibility of |
| 20:28 | · | faster-than light travel? This is a very good question to which the answer is: Quite possibly |
| 20:34 | · | nothing. I just used this as an example. It's an example to show that faster-than-light travel |
| 20:40 | · | does not necessarily imply time-travel paradoxes. The latter just doesn't follow from the former. |
| · | Quantum Gravity and Summary |
| 20:47 | · | To add one final reason why you shouldn't trust the argument that faster-than-light travel is |
| 20:52 | · | impossible is that we know our current theory of space-time, General Relativity, |
| 20:58 | · | can't be correct because it doesn't work together with quantum theory. This is why we need a theory |
| 21:05 | · | of quantum gravity, and we still don't have one. We know however that causality and locality become |
| 21:12 | · | really screwed up in quantum mechanics, and the same is probably the case in quantum gravity. |
| 21:19 | · | This is why I think it's extremely implausible that any argument about |
| 21:24 | · | faster-than-light travel would survive in the to-be-found theory of quantum gravity. |
| 21:29 | · | Of course you already know that no one's figured out how to travel faster than the speed of light. |
| 21:35 | · | But I hope I have managed to convince at least some of you that the formal reasons you may have |
| 21:41 | · | heard against it are on shaky grounds. This is why I believe physicists should think a little |
| 21:47 | · | harder about faster-than-light travel. At the very least, then maybe humans wouldn't be so boring. |
| · | Learn Physics on Brilliant 21:54-23:37 [redacted] |
