I think it's possible to travel faster than light. Here's why. (Patreon)

[This is a transcript of the video.]

I believe there’s intelligent life on other planets. And the most plausible reason why they haven’t contacted us is that we’re too boring. I mean, we haven’t even figured out how to send information faster than light. Pathetic.

But wait, let me guess. You’ve heard that it’s impossible to send information faster than the speed of light because, er, physics. Yes, I’ve heard that too. But I think it’s wrong. And in this video, I want to explain why. Is it possible to break the speed of light limit? That’s what we’ll talk about today.

If you’ve been following this channel for a really long time, first of all, thank you, I know it isn’t always easy. Second, you may remember that I made a video about faster than light travel already a few years ago. But I think no one understood it.

In fact, when I watched it again recently, I didn’t understand it either. So please give me a second chance. Because I think it’s becoming increasingly relevant to get this right. And this time, I’ll try to do it better. I’ll even let you leave the toilet seat up.

In the past year or so, there’s been a lot of talk about unexplained aerial phenomena, formerly known as UFOs. I don’t actually believe any of those are of extra-terrestrial origin because, as I said, we’re just too boring for aliens to bother visiting us.

Then again, what do I know? Maybe some of those aerial phenomena really are space probes from alien species. And if we want to properly evaluate how likely that is, we need to talk about the possibility of travelling faster than light, or at least sending information faster than light. Because if it’s possible at all, then that’s what the aliens are doing.

The idea that the speed of light is a limit comes from Albert Einstein’s theory of Special Relativity. Yes, this guy again. The speed of light plays a special role in his theory because it’s the only speed that’s the same for all observers. And just to make sure, I mean the speed of light in vacuum. The speed of light in a medium, any medium, is slower than the speed of light in vacuum, and depends on how you move relative to the medium. But the speed of light *in vacuum does *not depend on how fast you move because there’s nothing for you to move relative to.

I know this sounds about as exciting as flossing teeth, but it has some unexpected consequences, and I don’t mean that your crowns pop off.

Suppose you and your friend, let’s call him Bob, both have a water hose, and it spits out water at, say 10 kilometres per hour. Bob gets on a train which moves at 200 kilometres per hour. If you live in the United States, make that 20, then he turns on his water hose again. The water moves with 10 kilometres per hour relative to him. But how fast does it move relative to you? You’d expect it to be the speed of the water plus the speed of the train, right?

Now imagine you don’t have water hoses but laser pointers. They send out light with, well, the speed of light. Your friend Bob gets on a train again. In vacuum, of course. Because this is theoretical physics, where people don’t breathe, cows are spheres, and 3 is either equal to pi or infinity, depending on whom you ask. How fast do you see the light of Bob’s laser? You’d expect this to be faster than the light that comes out of your laser pointer by the speed of the train, but not so. It moves with the exact same speed as yours. Because the speed of light is always the same.

This is what was confirmed with the famous Michaelson-Morley experiment, and it has a very odd consequence: You can’t catch up with light. It doesn’t matter how fast the train is, light will still move away from it with the speed of light. If that didn’t make your crowns pop off you’ve probably heard it so many times before that you’ve forgotten how remarkable it is. That, or you have a very good dentist.

We can quantify the difficulty of catching up with light by asking how much energy it takes to accelerate an object. Let’s suppose the object has a mass m. This mass corresponds to an energy which is given by the most famous equation ever, E equals m c square, where E is the energy and c is the speed of light.

But now we accelerate this massive object from zero velocity to some other velocity, v. The energy you need for this acceleration is the total energy of the object at the new velocity, minus the energy it previously had. In Einstein’s theory, the total energy of an object that moves relative to you with velocity v is given by this expression.

Now if you want to know the kinetic energy, you take this and subtract the same expression for zero velocity. So you get this somewhat messy expression, but don’t despair, it isn't as bad as it looks.

For one thing, when the velocity, v, is much smaller than the speed of light, then the ratio v over c is much smaller than one. In this case, the complicated thing with the square root is approximately one plus one half v over c square, the one cancels out and the c’s cancel out and you get one half m v square, which you might remember is just the kinetic energy.

But we’re more interested in the case where the velocity gets close to the speed of light, so v over c gets close to 1.  Then this factor gets close to zero, and the entire energy gets close to one over zero, which is infinity.

This means if you want to accelerate an object until it reaches the speed of light, you need an infinite amount of energy. Another way to put this is that the only way you can move at the speed of light is when your mass is zero. Even a keto diet isn’t going to do that for you.

This is where the idea comes from that the speed of light is a limit that you can’t cross. But… this argument has some issues.

The first issue is that it doesn’t mean faster than light travel is forbidden in Einstein’s theory. Indeed, his theory is entirely compatible with faster-than-light travel. The problem seems to be instead that you can’t accelerate from below the speed of light to above the speed of light. It’s more like a barrier than a limit.

The second issue is more a peculiarity. It’s that on all other occasions when physicists see some quantity go to infinity, they’ll tell you that infinity is unphysical and a sign that the maths doesn’t properly work. Big bang, black holes, non-renormalizable effective field theory, whatever. If there’s a singularity, they’ll say it’s a mathematical artefact and not real. They don’t say that in this case, and I think they should.

The third issue is that we have a counterexample to the claim that one needs an infinite amount of energy to reach the speed of light, which makes the argument extremely suspect. But to see why I say this, I first need to tell you where mass comes from. No, it’s not too much cheese, it’s simpler than that.

Most of the mass of objects around you isn’t really mass, it’s binding energy. You see, almost the entire mass of atoms is in the nucleus. The nucleus is made of neutrons and protons, and the neutrons and protons are each made of three quarks. For the neutron that’s two down and one up, and for the proton it’s two up and one down. Quarks, not thumbs, I mean. The quarks do have masses, but if you add them together, the sum is far less than the mass of either the neutron or proton.

Instead, most of the mass of neutrons and protons is the binding energy from the strong nuclear force that holds them together. We *interpret it as mass because E equals m c square. But this means it’s really odd to put the mass of an object into this equation in Einstein’s formula. Because really if you look at the object microscopically, most of it isn’t mass. And, yes, that means most of you isn’t mass either. You’re almost entirely made of pure energy. Though when I see how much time you spend watching YouTube I find that hard to believe.

What’s with the remaining mass, the part that isn’t binding energy? Electrons and quarks do have masses, albeit very small ones. These masses come from the Higgs-field, not to be confused with the Higgs-boson. To be more precise, the masses come from the condensed Higgs field. This Higgs-field condensate fills the entire universe and drags on particles. It’s kind of like the 19th century aether, but with two important differences.

First, the aether was believed to be necessary for light to travel. But for the Higgs-field it’s the opposite. The particles of light, the photons, are massless, which means they don’t feel the Higgs field at all. But other particles do feel it. When the field condenses, it sticks to the particles. That slows them down and it looks to us like they have a mass.

Another difference between the condensed Higgs-field and the aether is that the Higgs-condensate looks the same for everyone, regardless of how fast they move. It’s just a number at each point in space-time and everyone agrees on what this number is. It’s like the number of socks in your washing machine. Doesn’t matter how fast the spin cycle is, the number of socks doesn’t change. Or if it does, I guess it’s time for new socks.

The aether on the other hand was believed to be basically like a fluid. Some people would drift with the flow, and some people would move against it, and they’d see different things. This is *not the case for the Higgs-field and its condensate. If you like technical terms, and I just know you do, it’s a Lorentz-scalar and invariant under Poincare transformations.

Ok, so the masses of fundamental particles come from the Higgs-field. But. This is only the case when the field is condensed and that wasn’t the case in the early universe.

Think of an early morning in spring. No, not the coffee, I mean the dew on the grass. Where does it come from? Well, air contains water vapour, which means that individual water molecules float around in the air. But warm air can hold more water vapour than cold air. If the air temperature drops during the night, the water molecules collect to form drops which are too heavy to keep floating, and they fall to the ground.

The Higgs field has done a very similar thing, not at night, but in the early universe. In the early universe it was really hot. There was a Higgs-field but it wasn’t condensed, kind of like the water vapour in the air. But then the temperature dropped, and the Higgs field condensed. This condensate now fills the entire universe. But it was only when the Higgs field condensed that particles acquired masses.

It’s a phase transition called “electroweak symmetry breaking” and it’s believed to have happened about 10 to the minus 11 seconds after the Big Bang at a temperature of 10 to the 15 Kelvin, that’s much hotter than even the centre of the sun.

What all this means is that in the early universe none of the particles had masses. They were all massless, and they were all moving with the speed of light. Later they were not. And here’s the important bit: The energy that was released in this phase transition was finite. If it hadn’t been, we wouldn’t be here, and someone would have written a paper about that, I’m sure. But the equation that we looked at earlier said that the difference in energy should have been infinite. What gives?

Mathematically it’s pretty obvious what goes wrong with the earlier argument. If you look at this equation again, you see that if this factor goes to zero, but the mass *also goes to zero, then the ratio can well remain finite.

This doesn’t help us at all to travel at the speed of light. Because we can’t just uncondense the Higgs field. Even if we could, it’d basically evaporate the traveller and, I mean, I’m not a doctor, but that’s probably not healthy. So, this isn’t going to let us build a warp drive. But it shows that the argument that the speed of light is a barrier isn’t even technically correct.

There is another reason that physicists often bring up for why you can’t travel faster than the speed of light, which is that it can allegedly cause time-travel paradoxes.

The argument goes like this. Suppose Alice observes a spaceship which goes by faster than the speed of light. Zoom there it goes. Her friend Bob can’t afford the new super-duper spaceship and lamely zooms by in last year’s model, at merely 90 percent the speed of light. Then Bob would see the space-ship going back in time.

Let's draw this into a space-time diagram to see why The horizontal axis depicts one direction of space, so left and right, for example. And the vertical axis is time. A spaceship which doesn’t move, according to this axis, just makes a vertical line. A spaceship at constant velocity is a line which moves at some angle. By convention a 45-degree angle is the speed of light.

Alice just sits there and moves on this straight line. And everything that happens on a perfectly horizontal line happens simultaneously, according to Alice.

The faster-than-light space-ship goes by like this. And Bob moves on this line. The question is now what Bob sees. For this, let’s look at two particular events. And let’s make sure those events have a clear arrow of time from entropy increase, let’s say someone drops a raw egg. The guy in the spaceship stumbles here, and the egg smashes to the ground here. This means, importantly, that time on the space-ship passes in this direction, and *not in the other direction.

Since Bob is moving relative to Alice, he sees different events happen simultaneously. I explained this previously in my video on why the past still exists. So, well, either take my word for it or watch the other video.

For Bob, events that happen at equal times are on these straight lines, not on horizontal lines. You can then see that for Bob the order of events is that the egg first smashes to the ground and then gets dropped. It seems that for Bob the time order of the faster than light ship is reversed, crazy!

The first reaction you may have to this is: Who cares what Bob sees? I mean you can watch this video in reverse and that doesn’t mean I actually spoke in reverse. Fair enough.

The second reaction is to point out that this isn’t what either Alice or Bob see anyway. You can’t see a faster than light ship coming for the same reason you can’t hear a supersonic plane coming. What do you want to see it with? Instead, both Alice and Bob will only see the spaceship after it’s gone by and then they’ll see it moving away in both directions. And again, you can say, so what? I mean gravitational lensing distorts galaxies into rings, alright, but that doesn’t mean the galaxy is a ring. It’s just some weird trick on our perception.

And that’s entirely correct… But, you know, physicists have noticed that too. Thing is, this wasn’t the entire argument. There’s a piece missing which goes like this.

Imagine you are Bob, and there’s really a spaceship that can go faster than light and according to you that goes back in time. Let’s not ask what this means but what you can do with it. If the time on the spaceship really goes forward this way, then you can give a message to the guys as they come by. They take your message to Andromeda, hand it over to another faster-than light spaceship, and the second ship brings the message back to you. It would then arrive before you sent it.

This means you could send messages to yourself back in time, and *that causes a lot of trouble. Imagine that this video greatly disturbs you and you send a message to your younger self to not watch it, then you’d never have sent the message in the first place, so did you, or didn’t you watch it? This type of construction is also called a time-like closed loop, it’s a loop in time.

The argument then concludes that if faster-than-light travel was possible, that would lead to causality paradoxes, so it must be impossible.

But this argument is also wrong. The reason is that just because according to Bob there’s a spaceship going that way with a time that goes forward on the space-ship in a direction that Bob calls backwards in time, that doesn’t mean if a space-ship goes that way then its internal forward-in time direction would be that way. If the time-direction on the ship goes that way, they can’t deliver a message to your younger self. Instead, your younger self can send a message there, and nothing’s weird about that.

Physicists do have a reason to assume that time on the space-ship could go this way, but it’s not a good reason. It’s because in special relativity all observers must be treated the same. In Special Relativity, if you think that this is possible, then this must also be possible.

But Special Relativity is special because it doesn’t contain gravity and this means it doesn’t actually describe reality. For this, we need general relativity. And while the time-travel argument is correct in special relativity, it is not correct in general relativity.

I know this video is some tough going so let’s stop for a moment to appreciate where we are. I summarised the usual argument for why faster than light travel leads to time-travel paradoxes. I’m about to explain why this argument doesn’t apply in the real universe.

The usual argument uses special relativity according to which only relative velocities are physically relevant. In special relativity, you can’t be at a velocity of absolute zero, that just makes no sense. But the real universe contains stuff, as you’ve probably noticed. You can take all this stuff, calculate the average velocity that it moves with. And then you can define absolute rest to be motion that has no relative velocity to the average of all that stuff. Since you like technical terms so much, it’s called the “co-moving frame”. It’s the reference frame that moves along with matter in the universe.

We are currently not at rest relative to the average of stuff in the universe because the earth goes around the sun and the sun goes around the centre of the milky way and the milky way is rushing towards something called the big attractor that no one really knows what it is. If you wanted to be at rest with the universe you’d have to run at 300 kilometres per second into this direction. No, wait. This. Or, this?

Alright, so there’s matter in the universe that moves one way and not another. But what does this have to do with the time-travel story? Suppose you are Alice again but now you are Alice in a universe with general relativity and you are moving with the stuff, you are in the co-moving frame. And now assume that faster than light travel is only allowed forward in time in this particular frame. In this case you can’t make loops in time, regardless of what Bob thinks he sees. The co-moving frame defines one direction as forward in time. The only thing Bob can do is send two signals to Andromeda, and there’s nothing Paradoxical about that.

You may wonder now what the motion of matter should have to do with the possibility of faster-than light travel? This is a very good question to which the answer is: Quite possibly nothing. I just used this as an example. It’s an example to show that faster-than-light travel does not necessarily imply time-travel paradoxes. The latter just doesn’t follow from the former.

To add one final reason why you shouldn’t trust the argument that faster-than-light travel is impossible is that we know our current theory of space-time, General Relativity, can’t be correct because it doesn’t work together with quantum theory. This is why we need a theory of quantum gravity, and we still don’t have one. We know however that causality and locality become really screwed up in quantum mechanics, and the same is probably the case in quantum gravity.

This is why I think it’s extremely implausible that any argument about faster-than-light travel would survive in the to-be-found theory of quantum gravity.

Of course you already know that no one’s figured out how to travel faster than the speed of light. But I hope I have managed to convince at least some of you that the formal reasons you may have heard against it are on shaky grounds. This is why I believe physicists should think a little harder about faster-than-light travel. At the very least, then maybe humans wouldn’t be so boring.

​When I was in middle school my physics teacher told me that very few people understand Einstein’s theories. Maybe that was once correct, but I can very confidently tell you that it’s no longer the case today. I believe that everyone can understand Einstein's theories today, but passively watching YouTube videos won’t get you there. You have to actively engage with the material. Our sponsor Brilliant can help you with this.

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