Is it possible for anything to travel faster than light? What about tachyons? How would faster-than-light travel break causality? And just what the heck is causality, anyway? I discuss these questions and more in today’s Ask a Spaceman!

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Hosted by Paul M. Sutter, astrophysicist and the one and only Agent to the Stars (http://www.pmsutter.com).

EPISODE TRANSCRIPTION (AUTO-GENERATED)

some ideas are so fundamental to physics to science itself that they don't even appear in science itself. It's It's like the foundation of a building. You can see the building doors, windows, walls, roof the usual, but you don't see the tons of concrete below the surface or, in the case of skyscrapers, the giant pillars that they drive hundreds of feet into the ground to support the structure. I've shared on this show all sorts of cool physics and astronomy, and sometimes I've shared the guts. I don't just show you the paintings in a house or the cool architecture. Check out that skylight. Sometimes I bust open the walls and show the electrical wiring and the plumbing. And sometimes we dig a deep dive into the septic system like we did with nine episodes on the meaning of quantum mechanics. But my goal with this show is complete knowledge of time and space, and if we just stick to what's happening above the ground, we're gonna miss a lot. So today we need to talk about foundations, about basements, about blocks of concrete.

We need to talk about causality. Causality is so simple, so obvious so immediately in your face. True that it shouldn't even need to be talked about. It's simple. Every effect must have a cause, and every cause must come before every effect. I have to swinging a bat before I can hit it with a ball. You can only feel someone after they touch you. The sound of two cars crashing only happens after they've hit each other. I have to eat the slice of cheese before I can taste it. You can't think a thought that you haven't had yet. Causality encodes. It enforces our everyday experience of the world. Every interaction among us, humans and every interaction among all the particles of the universe obey this simple cause and effect relationship. Causality allows us to build our conceptions of past and future because causality, in a sense, what we use to determine the flow of time. It's the dividing line causes always precede effects.

They always come before effects, and those effects become new causes that lead to new effects and on and on and on. And that's how the universe organizes itself. What we call the past is just the set of all the causes that have led to the current situation and what we call the future is the set of all possible effects. Given the current set of causes. Now there is an entire branch of metaphysics that digs into why causality exists and even whether it exists in the first place. And that is whether our universe is really random and is our conscious observations that enforce an ordering on it so that our biological systems can get things done, like eating food and browsing social media. And while I have an enormous amount of respect for philosophy, I will say again and again how important those kinds of questions are, because without those questions, we can't ever truly organize our own thinking and dig into the the deep roots of our existence. I am, unfortunately, not a philosopher of metaphysics. So if we can't talk about the metaphysics of causality, we have to talk about the regular physics of causality.

And in regular physics, causality is everywhere. Causality is such a foundational concept that there's not even an equation for it, or a theory for it or a formula for it. There's not a solution for it. Causality simply is, and it underlies the whole thing. every single statement we make in physics and astronomy. And in fact, all of science assumes causality to be true. That causes lead to effects. That's how we go about our business. We see an effect in nature, and we try to figure out the cause, That's it. And Einstein being the somewhat brilliant person that he was recognized, that causality is so simple and so fundamental. And then if we're gonna assume it's true anyway and use it to build our entire physical intuition of the natural world, Well, why don't we use it to literally build an intuition of the natural world? Like, literally. What if we encoded the concept of causality in the theory of physics?

And it was his insights into the nature of causality that allowed him to build a foundation. That foundation we call special relativity and the entirety of modern physics is built on that foundation. Special relativity does something special. It directly addresses the concept of causality in physics. It takes it at face value. It asks what is causality? What does it mean for one cause to create an effect? And what are the limits of what effects a cause can have. What are the limits of something I can do if I'm here in the universe? What are the limits of what I can influence of what I can affect? Einstein found that special relativity addresses this issue of causality by uniting space time and defining their relationship. And Einstein used causality to tell us how space and time are connected. The first step is that space and time really are connected.

We are so used to thinking of movement in space as separate than the flow of time. You go around, you walk around the room, you go to work, you go to the grocery store, you play with the kids. Whatever you live your life, you exist. You move around in space all the time, huh? I? I did not intend that joke, but that was a pretty nice one. And you also move into your future. We move from past to future. We we we do this automatically. We were used to thinking of these motions as independent. You'd simply move through time and you move through space. Einstein found that we can't think of space time as separate. We have to think of them as United there is one entity known as space time. There is one single entity known as space time. We are all moving through space time together, and in fact we're moving through space time this united four dimensional fabric at the speed of light. That's right. You right now are moving at the speed of light, but not in any of the spatial directions Not left or right or up or down, or forward or backward.

You're moving into your future at the speed of light. If you are perfectly stationary, you are still moving at the speed of light through the dimension of time. If you start moving through space, even just a little bit, that takes away some of your speed that you're moving through time. The faster you go in space, the slower you move. In time, moving clocks run slow. This is all a byproduct of the unification of space and time, Einstein found. But because of this relationship between time and space, this united fabric that we call space time that the speed of light defines causality. It defines the fastest way that I can influence something else because it sets a speed limit. If everything is moving through all of space time at the speed of light. Then that means I can't go faster in space than the speed of light.

That is the maximum speed limit. Because that is the speed limit that everything is traveling at because we all move through space time at the speed of light. Causality has a limit. If I want to influence you if I want to be a cause to your effect. If I want to effect change in my universe, I am limited by the speed of light. That is the fastest that I can change the universe that I can cause and effect. I can't go faster than the speed of light and to explore why the speed of light is the limit. We need to talk about one weird trick. You see space and time, they're united. But they're united in a very strange way in this strange way. Well, it doesn't sound very strange at first, but it's going to have enormous consequences for literally everything else. The reason that the universe has this speed limit of the speed of light.

The reason that the faster you go in space, the slower you go in time is a minus. Sign? Yeah, a minus. Sign. You heard me, right. Check this out. You ever draw a triangle? Especially one of those right triangles Has a little right angle in it, you know, two straight legs perpendicular to each other, and then a long angled line connecting them. Do you remember the Pythagorean theorem that tells you the relationship of the lengths of those sides of the triangle? If if you have three sides to the triangle with three different lengths, we'll call them a B and C. Then you know that a squared plus B squared equals C squared the Pythagorean theorem? Yes. I note the Pythagorean thought that relationship was so special that they basically worshiped it as a part of their religion. And I don't blame them because the fact that this is true is pretty astounding. It represents one of our first recognitions that some things in the universe are truly universal, but that's that's a different episode. This Pythagorean theorem. You can draw a right triangle. A squared plus B squared equals C squared that holds for space, but not for space time.

You see, if I replace one of those legs. With time, I get a different relationship instead of a squared plus, B squared equals C squared. If I take out one of the legs and I say that leg is not laying along a spatial dimension, it's, uh, laying along the path from past to future. We'll call it T For time. That seems pretty convenient. It's not a squared plus T squared equals C squared. If I draw that triangle in space time and one of those dimensions is time, it's not a squared plus, T squared equals C squared. It's a squared minus. T squared equals C squared. Now, first, this is no big deal, but this minus sign, uh, propagates. You see, Einstein discovered the fundamental relationship between space and time. He found that they are connected not through the usual Pythagorean relationships that we know of in space. But through this minus sign, he discovered that connection, and it shows up everywhere where relativity is involved, which is like everywhere, and it really messes things up.

For example, let's say you wanna go faster than the speed of light. I won't get into the mathematics, but Einstein with this relationship, this a squared minus T squared equals C squared was able to figure out that there is a universal speed limit to the universe. And it goes like this. Let's say you're starting perfectly stationary and you give yourself a little Oh, you got a little rocket and it, you know, blasts out one end, you go faster. But when you move, you don't just have your mass. You also have your kinetic energy of motion and equals MC squared energy equals mass times the speed of light squared You energy is mass. So as you go faster, you are literally more massive. You are literally heavier when you go go for a walk, You literally weigh a little bit more than you do if you're perfectly stationary. But if you're heavier and you blast out your rocket, you give yourself another little burst because you're heavier. You don't get to go as fast again. There's, uh, like dim, diminishing returns.

The faster you go, the more energy you have that is equivalent to having more mass. And so it gets harder and harder to push you now. Without relativity, you could just keep going if space and time were connected by the Pythagorean thing you could. You could go as fast as you want. You could go up to infinity, but that minus sign shows up. It pokes its little head in. And the way all the math shakes out is that as you try to approach the speed of light, that minus sign creeps in in a very, very nefarious way. And it causes your energy to climb at a ridiculous rate, the closer you get to the speed of light. And if you try to get to the speed of light, you end up having infinite energy, which means you have infinite mass, which means it's impossible to move you. If you are traveling below the speed of light. It takes an infinite amount of energy to accelerate you to the speed of light. That's the nutshell and the limitation of the speed of light. Why? There's a reason I went through all this minus sign introduction stuff because the limitation of the speed of light isn't like the limitation of the speed of sound.

It's not some matter of engineering or cleverness or some weird trick of the universe. The limitation of the speed of light is baked into the structure of space time itself. The relationship between space and time gives us a universal speed limit. It happens to be the speed of light. It could have been any number. It happens to be the speed of light for other reasons. And so the speed of light defines the maximum speed at which you can move in our universe. And we are all moving at that speed through all of space time. And because of this minus sign relationship, the faster you go in space, the slower you go in time. And so the fastest you can go in space is the speed of light, and this becomes the maximum speed at which causes can lead to effects. It's the maximum speed that events can influence each other across the universe. The speed of light is the speed of causality. This fundamental relationship between space and time that Einstein discovered defines the limit of causality in our universe.

All effects must propagate at or below the speed of light. It is just that simple. It's that it that's it, that's it. You can't go faster. Effects cannot go faster than that. And that means if we could go faster than the speed of light. Then causality itself breaks down, and we can see how this works. But playing with a thought experiment involving a strange new kind of particle, the TA this show is sponsored by better help. One of the most awesome things about physics is that it's like a user manual for the universe. You can literally use it to predict the future Now. Now, humans are a little bit more complicated. Believe it or not, people are more complicated than quantum physics. I am not joking, and and life and dealing with people does not come with a user manual. And the next best thing is therapy. I have been using therapy for years. It's such a powerful tool for me to to answer life's questions when those questions don't come in the form of of of physics problems.

And I think you will benefit a lot from it, too. And that's why I'm proud to have better help as a sponsor. Better help is the world's largest therapy service. Better Help has matched 3 million people with professionally licensed and vetted therapists available 100% online. Plus it's affordable. Just fill out a brief questionnaire to match with the therapist. If things aren't clicking, you can easily switch to a new therapist any time. It couldn't be simpler. No waiting rooms, no traffic, no endless searching for the right therapist to learn more and save 10% off your first month at better. Help dot com slash spaceman. That's better help HE LP dot com slash spaceman The tache is a particle that can travel faster than light. We're gonna define the tache to be a particle that travels faster than light now faster than light particles have been played with and toyed with and thought about ever since Einstein himself. He called them meta particles, by the way.

But the word comes to us from physicist Gerald Feinberg, who named them after the Greek word for Swift when he was playing around with the idea in the 19 sixties. Uh, he also called particles that travel at light speed. Like photons, he called them Luxon and particles that travel below light speed. Like everything else. Patreons that's patreon dot com slash PM Sutter P MS U TT ER It is your contributions that keep the show going, and I truly appreciate it now is a good time to go. Contribute patreon dot com slash PM Sutter. No, he called them Radon's from the Greek word for slow. But but Luxon and radon didn't exactly catch on, but TAKS stuck and tas are weird. If they were to exist, they would always travel faster than light. They would be born traveling faster than light, and they would die traveling faster than light. They could never, ever go below the speed of light. In fact, they would have just as much as a hard time approaching the speed of light as we do. But their trouble would be slowing down.

The slower they go, the more energy they acquire. It's the opposite for us. The faster we go, the more energy we acquire, the more mass we have and the harder it is to climb the next ladder to get closer to the speed of light for ta ons, the faster they go, the lighter they are, and as they try to slow down to the speed of light, their mass increases and they have a harder time reaching it. For tachyons, decelerating, not accelerating. Decelerating to the speed of light requires an infinite amount of energy, and on the outset there's nothing preventing their existence. After all, we have below light speed particles we have at light speed particles. And there's nothing in the math of special relativity alone that says that TAKS faster than light particles, shouldn't or couldn't exist. Instead, we only learn that they can't exist, that tachyons can't exist. Once we take the raw concept and put it through the paces. Let's briefly or should I say, tachyon, take them seriously and see what it would mean for the universe if TAS did exist.

This is an important step in developing new ideas. You can have any crazy idea you want in science. Seriously, all are welcome, but you need to take your crazy idea seriously and explore its consequences. What does it actually mean? And if something ugly turns up, you need to give up your idea. So to explore, we've we've we started this episode by saying the very structure of space time the relationship between space and time, sets an upper limit to causality, and that the reason we have causality is this structure of space time. So let's see how faster than light particles like tanks break that idea of causality. Let's begin by deciding which one of us is going to blast off on a special space ship for a tour of the galaxy. Since I'm the one hosting the show, I need to stay down on Earth to continue writing episodes. That means you're the one to go kiss your family. Goodbye. It's time to get packing. Say you go in your spaceship, you blast off, you fly away and you're on some distant planet.

It doesn't matter where. Proxima Trappist one You know, pick your favorite exoplanet and park yourself. Now you're there. You've set up home maybe little ranch planting some crops on your new world. But you still want to listen to the latest episode of Asa Spaceman. Now, if you have a telescope and you could point it back to me and you were creeping in through my office window, you could see me record the episode and hit the send button, right, because I am constantly emitting light or light is reflecting off of me from the sun. And then that light is continuing its journey out into space. And if you could zoom far enough away, you could watch me as I record an episode. And if I press the send button to emit my episode and I send that episode to you, I want beam it to you a special subscription. Highest tier for interplanetary adventures.

If I send you that episode through normal radio waves, you would receive that podcast. You would receive that message the same time, or shortly after you see me pressing the button so I would press the button. It would emit the radio signal. The radio signal would race across the galaxy at the speed of light and you would receive that. And now, if you're looking through your telescope, you could watch me record the episode, press the send button. And then shortly after Bing the new episode, your smartphone vibrates and the episode is ready for you to download. It has received the message containing the information on my podcast. The cause leads to the effect you see me press the button, and then you get the message right. Everything's super straightforward, but if instead I decide to use a tack on transmitter, then something different happens now. From my perspective, nothing is special. I record my episode I hit send and it blasts off to you, not riding waves of radio.

But But tack on beams, whatever these particles are, I can create them. I encode my message. My episode, uh, in those tas and I send them off to you flies off to you somewhere in the galaxy. You receive my latest episode sometime later, and then you listen to it. From my perspective, everything's fine. I had a cause which was pressing. The send button led to an effect, which was the transmission of the episode. Yeah, it got to you faster than light, but who cares, right? This is every single science fiction show Oh, we need to communicate with with the home base, you know, use the the the the sub light on whatever transmitter, and they just instantly have a a two way like Skype phone call or a zoom conference meeting of the future happening faster than light. And it's no big deal. From your perspective, though, something different happens because I use faster than light particles to send my episode to you. That signal raced ahead of the photons that carried the image of me pressing the button.

You would get my latest episode, start listening to it because it was transmitted to you faster than light. And then you would look through your telescope and you would see that I haven't sent the episode yet. That's because the light that carries the information, the image of me recording the episode and pressing the send button is going slower than the actual message itself. You would see that I I'm still in my pajamas or eating my lunch or actively recording them. So whatever it is, you haven't seen me hit this end button. You're sitting there listening to my episode before you even see my lips moving to record the episode. The information of me pressing the send button is delayed compared to you actually receiving it. This is highly weird, but this isn't the ugly part yet. You see, it's not the ugly part because you know that even though things appear out of order, you can use the math of special relativity to calculate when things actually happened.

You're an observer. You're somewhere in the distant universe. And, yes, you received my podcast before you saw the image in your telescope of me pressing the send button it looks like things are out of order because I have to hit the send button. That is my cause. And that has to proceed. The effect of you getting the message. You received it in a different order. But that's OK in special relativity, because you can retrace the TAS path in the photons path, the ta on path that carried my episode and the photons path that carried the image of me pressing the send button. You can deduce that even though the TA arrived before the photons because they traveled faster than light, but they were sent at the same time. Or at least you can deduce you can do the math, that the machinery of special relativity minus signs and all allow you to calculate that. Aha! When you eventually get the image of me pressing the send button, then you can calculate all the distances and times and lengths and all that, and you know that I still sent the signal.

I press the button, and then the tas raced ahead. Even though you got the ta ons first, it doesn't mean I sent them first. These kinds of calculations happen all the time in relativity because in relativity, signals get mixed up all the time anyway. Even going slower than the speed of light, it's possible to exchange before and after you can rearrange the ordering of events. Depending on your perspective, that is fine. That's normal and special relativity. But that's just your perception of the events, which is different than the actual ordering. One of the points of special relativity is to take everyone's different observations and find a unifying framework. You can use the machinery you can use the mathematics to say OK, even though I observed from my position on this distant planet that the message came before Paul hit send, I can use the mathematics of relativity to figure out OK, He actually did send the message before the message blasted out and reached me. But then you decide to leave your planet and start moving.

Let's say you're moving away from me and nice and fast, too, something close to the speed of light. A couple of weeks have passed. You're still traveling, still cruising close to the speed of light, and it's time for the next episode from my perspective again, everything proceeds as normal. I write an episode. I record an episode. I press the send button the track. The the tack on transmitter beams it off to you. The ta go racing away and eventually catch up to you. It takes a little longer now because you're moving away from me, but they still make it. You have received my episode, and everything is right with the world. But something funny happens from your perspective. And that funny thing is because of the relationship between space and time. Moving clocks run slow. The faster you move in space, the slower you move in time. From your perspective, however, cruising along on your rocket ship, you appear perfectly still. Remember, all motion is relative from your perspective. You are perfectly still and the universe is moving. All motion is relative in your frame of reference. Cruising along on your rocket ship.

You are not the one moving. It's the universe that is doing the moving. There is no experiment that you can perform that you can use to deduce that you are moving. That is the point of relativity. So you get to say that you're the still one in the universe is moving in particular I'm the one moving from your perspective. According to you, I'm the one moving away from you. You're not the one moving away from me. This is allowed in relativity. And because I'm the one moving, I'm the one who's going slow. From my perspective, you're the one going slow from your perspective. I'm the one going slow. Well, we're gonna focus on your perspective from your perspective. I'm the one going slow, really slow because of time dilation, moving clocks run slow. According to you, I am racing away. And so my clocks have slowed down. I appear to be moving in slow motion like I'm swimming in molasses or something when you receive my TA on episode and look through your telescope to see what I'm up to.

I'm not recording the episode. I'm not writing it. I'm not having lunch before. I'm not going to bed in the night before. I'm weeks away from even thinking about the episode, let alone recording it. And yes, I'm getting a little weirded out at your constant invasions of my privacy, but we're gonna let it go for the rest of this episode. I appear to be grindingly slow and Yes, you have received my podcast. So you know, I sent it. But from your view in the telescope, about what? Of what I'm doing, I am still weeks away from sending it. And if you go fast enough above a certain threshold, something goes haywire. When you go through the math of relativity to figure out the correct order of events and that speed fast enough, the exact speed depends on how quickly the tache ons are going and how far you are away from me. But at some speed, there is some threshold where time dilation stretches things out so much that even when you do the math of relativity to figure out the correct ordering of events, you get the wrong order of events.

I am so slowed down from your perspective that not only have you received the TA before I sent it, but you calculate that the TA was sent before I sent it. That's how behind I am. That's how slow I am from your perspective. It's not just a trading places in your perspective. It's a trading places in all perspectives. The has traveled into its own past, and it can do that in a very special set of circumstances. If you, the receiver, are moving away from me fast enough to cause me from your perspective to slow down so much from time dilation that there is no way that I could ever catch up and send the signal in time you see tak ends don't just go faster than light. They go faster than causality, the flow of time, the rate of flow of time. How fast a second is depends on our movement in space, and that's capped by the speed of light.

The speed of light is the limit of how quickly one event can influence another event. How quickly a cause can lead to an effect, and it's baked into the structure of space Time itself. The speed of light sets that upper limit on causality. And because tachyons go faster than light, they end up traveling into their own past. In a sense, if you go faster than light, you go faster than time itself because the rate of flow of time is capped at the speed of light. And if you go faster than that, you're beating time below the speed of light. I can always always always reconstruct the correct ordering of events, regardless of how I perceive them. The mathematics of special relativity. The machinery allows me to do that to rescue that, to say, man, my perspective is really messed up. Things look like they were flipped around. I received Paul's Taian episode of Ask a Spaceman before He hit Send, But that's just what I it looked like to me. Let me plug in.

OK, Einstein, come here. Give me your math, OK, we do OK. He hit send and then the message went out. But once you go above light speed, the machinery breaks down and it reverses causality itself breaks down to test this. Let's say you have your own tachyon transmitter. As soon as you hear my episode, you send me your reply and you say, Paul, Paul, you've done great work. The latest episode is just perfectly mind blowing. I am leaving my fortune to you via Patreon. Take a few months off. Go on a vacation, write a new episode later. You deserve it. That message races away from me faster than light and it reaches me, and if you send it quickly enough, it can reach me before I recorded my latest episode and sent it to you. Remember, ta ons travel into their own pasts. But if I hear the message, I don't write the next episode. I don't record it. I don't press send. I just go on vacation. There's nothing but an empty office in your telescope. But in order to get that message, you had to hear my latest episode, which required me to write it, which required me to record it and send it.

You literally watched me record it through your creepy time spy telescope eventually. But since your donation arrived in the past, it stopped me from ever recording it. So which is it? Did I record the episode or not? Did I hit the send button or not? The only way I can receive your response is if I record the episode. But if I receive your response, I don't record the episode. This is a paradox, and these paradoxes always appear whenever you try to violate causality. There are so many examples you can concoct, like killing your own grandparents, and then you don't exist. But if you don't exist, how can you go back in time? to kill your own grandparents in the existence of tachyons permits those paradoxes because you can use these messages that travel into their own past to alter the past. But the past has already happened. It's the set of all the causes that lead to the current effects. And if we change those causes, how do we have these current effects? Particles that travel faster than light can travel back in time, and if they travel back in time, they can break causality.

And why does going faster than light allow time travel into the past? Because special relativity bakes the notion of causality into its very mathematical bones, it's the very foundation of the theory. The basement, the cinder blocks, special relativity uses causality to construct our understanding of the relationship between space and time, and it uses the speed of light to set the upper limit of causality. It sets a number of limit to the flow of time faster than light is faster than time itself. Going faster than light allows messages to be sent into the past, and once that happens, our notions of cause and effect break down. Causality is the foundation of special relativity the speed of light. That limitation is baked into the fundamental relationship between space and time, and that fundamental relationship tells us how causality works.

What is the upper limit to the speed of causality? How quickly can one event influence another? And that limit is the speed of light. And if you go above the speed of light, you can travel into the past because you can find interesting frames of reference where ordering of events gets mixed up. And that's not just from your perspective, that becomes a universal truth, and you deduce that TAKS can travel into their own past. And if you can travel into your own past, you create paradoxes. You break down, cause and effect you, you break down causality. And if the foundation troubles, the house cannot stand. Causality itself does not appear in the mathematics of special relativity. Instead, causality. The fundamental concept of causes leading to effects is what Einstein used to construct special relativity, to preserve cause and effect, and to look at the relationship of how events can influence each other. That is how he built relativity, and it's built into the fabric of space time itself.

We haven't ever directly tested causality. We But we've tested special relativity and we've tested literally every other aspect of physics that rests on causality, which is all of physics. If you break causality, you break our entire understanding of the universe. It seems that causality is ingrained not just in the human experience of the world but into the fundamental fabric of space time itself. So no tas don't exist. And not because I'm a curmudgeon who doesn't like cool science fiction ideas. I love cool science fiction ideas, but the moment you allow travel faster than the speed of light you allow travel into the past and you break causality and nobody wants to break causality. Thanks to Amber Q on email. Nele von Patreon Brock P on YouTube Justin on email Randy W on email part J on email at Jonas and Twitter Sorry if I butchered that Courtney H on email Campbell Deon email at Danny Grieves BMW on Twitter and at great big Dumb You're not dumb at all on Twitter.

Keep sending me questions. And of course, thank you to all my patreon contributors. My top ones this month. You know who you are. Justin G Chris Barber, K Duncan, M Coy, D Justin Zra, NAIA Scott M, Rob H, Justin Lewis M John W, Alexis Aaron J Gilbert M Joshua John S, Thomas D, Michael R and Simon G. Patreon dot com slash PM Sutter, Your cause can have an effect of supporting this show and keep sending me questions. Hashtag ask a spaceman. Ask us spaceman at gmail dot com. All the usual places to go, and now we'll see you next time for more complete knowledge of timing and space.

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