# I finally understood why you can't go faster than light! (My mind is blown) - Channel: [FloatHeadPhysics](https://www.youtube.com/channel/UCGfFUc6eWxfbtjYeun6r9xg) - Published: 2023-11-16 - Source video: [Watch on YouTube](https://youtube.com/watch?v=Vitf8YaVXhc) - Read on ReadTube: https://www.read.tube/p/videos/Vitf8YaVXhc - Language: English ## Summary **Why Light Speed Is Impossible** The video explains why no object can be accelerated to the speed of light by building up the idea of time dilation from Einstein’s photon-clock thought experiment. As an object moves faster, light and other force-transmitting effects take longer paths in an outside observer’s frame, so clocks, radioactive decay, and even acceleration itself appear to slow down; near light speed, reaching the last bit of speed would require infinite time or infinite energy. The core argument is that the speed of light is the same in every reference frame, and that fact forces moving clocks and physical processes to slow down relative to outside observers. Using a photon clock, the video shows that the light pulse takes a longer diagonal path when the clock is moving, so the ticking rate drops. The same logic is extended to real clocks and to atomic and radioactive processes, with experimental evidence such as atomic clocks on airplanes and faster-than-expected muon lifetimes supporting special relativity’s time dilation. The video then argues that time dilation is not just a clock effect but a property of all measurable processes. Since radioactive decay and biochemical reactions also slow down for fast-moving objects, a moving person would age more slowly than someone at rest. The presenter uses this to justify treating time itself as dilated, rather than merely saying that hidden mechanisms are slowed. From there, the explanation of the light-speed limit becomes straightforward: if a spaceship is continually accelerating, an outside observer sees that acceleration diminish as speed rises because the signals and forces responsible for pushing the ship have to propagate across the ship at light speed. Near light speed, each extra gain in velocity takes longer and longer from the outside frame, so reaching exactly light speed would take infinite time. If the ship tries to maintain the same observed acceleration, it would need ever-growing fuel and force, leading to an infinite energy requirement. - Photon clocks show why moving clocks run slow. - Real clocks, atomic decay, and muons confirm the effect experimentally. - Time dilation grows stronger as speed approaches light speed. - Acceleration itself appears to weaken from an outside frame because force transmission is delayed. - Reaching light speed would require infinite time or infinite energy, so massive objects cannot get there. ## Article ### Why nothing can ever be accelerated to the speed of light Why can’t you ever accelerate any object to the speed of light? I mean, we can go very close, but we can never, ever reach the speed of light. Why is that? The most common explanation I get is: if you take the graph of kinetic energy versus speed, as the speed approaches `c`, kinetic energy goes to infinity, so it takes infinite energy. But my problem is that that is not an explanation. I do not have an intuition behind why that is true. Another explanation is that mass goes to infinity. But again, there is no evidence for that. So what is really going on? What is physically happening that is limiting that ship from going toward the speed of light? That is what we want to try to answer in this video. So if you are ready for it, let’s begin. ### Einstein starts with a photon clock Einstein says: imagine you are inside a very fast-moving ship and you have a photon clock with you. At this point I say: where is standard Einstein? I do not want to deal with hypothetical clocks. I want to talk about real clocks. Einstein says: patience. If you understand photon clocks, you will be able to understand everything else. I am like, okay, cool. Let’s trust him. So what is a photon clock? It is a clock where you have two mirrors and a photon bounces between the two. We can say that when the photon hits the bottom mirror, that counts as a tick. So we get tick, tick, tick, tick, tick, and so on. Now Einstein asks: what would the same clock look like if you are seeing the whole thing from outside? Well, let’s see. At first I am like, hey, it looks the same to me. The photon is bouncing between the two mirrors. But Einstein says if you look carefully, you see that the photon is now traveling a diagonal path. This means it is going to travel a longer distance. But remember, the photon always travels at the speed of light. The speed of light is the same in all reference frames, which means the photon is now going to take a longer time between the ticks. In other words, we will see that the photon clock ticks slower. So again, let’s compare: - From inside the ship: tick, tick, tick, tick. - From outside: tick, tick, tick. You can see it has become slower. And now what happens if the ship moves even faster? Well, it will travel an even longer path, as you will see, and therefore the ticks will become even slower. So the photon clock shows that clocks slow down when they are moving. ### Why real physical clocks slow down too At this point I say: cool, photon clocks take longer. That is great. But what about real physical clocks? Einstein says: if you look at this clock and zoom in to the second hand, what would the animation look like from the atomic scale? And I say: well, if the second hand is just sticking like this, then the animation would look something like this. But Einstein says that cannot happen. You cannot have something like this. The reason is that when this atom accelerates, this particular atom accelerates, all the other atoms cannot accelerate at the same time. Information takes time to travel. These atoms are bonded electromagnetically, so when one atom accelerates, we need to wait for an electromagnetic wave to go from one atom to another, and only then can the other atom accelerate. An electromagnetic wave is basically a photon. So the better way to think about this is: when this atom accelerates, it actually sends a photon, and only then the next atom accelerates, and then the next one, and the next one, and so on and so forth. So the whole thing is not instantly going. It is so fast that it feels like it is instantly going. But now Einstein asks: what if this set of atoms were moving? What would the animation look like now? Wait a second, this is also very similar to the photon clock, which means if this was moving, the photons would end up taking a diagonal path again, and therefore the whole thing slows down. Let’s look at it. Here we go. Yes, the photons are slowing down. The photon is not slowing down; the transfer is slowing down because the photons are taking a diagonal path just like before, and therefore real physical clocks actually slow down. Look at this: this one is ticking slower than this one. Real physical clocks slow down when they are moving. ### Evidence that time dilation is real At this point we ask Einstein: is there evidence for this? This is just a theory, right? Einstein says: well, probably not in his time, but today we do. You see, we have taken atomic clocks, which are synced on Earth, and then we put them on planes, and then we flew around the world, and then we brought them back. They went out of sync, and we did this multiple times. Every time we checked, we saw that the amount they went out of sync is perfectly predicted by special relativity. Of course, gravity also affects it, which is dealt with in general relativity, so there is this additional effect happening. But when you put all of that together, there is evidence that suggests that time dilation is real. So with this we know that time itself is slowing down, or is it? You see, clocks are slowing down, but how does it tell us that time itself is slowing down? Einstein says: for that, let’s look at radioactivity. ### Radioactive decay, half-life, and muons Radioactive decay is where you have an unstable atom that spontaneously splits. The cool thing about radioactivity is that they have something called the half-life. For example, if you take a radioactive radium isotope, it has a half-life of about 1,600 years. Which means if you take a billion radioactive radium isotopes, wait for 1,600 years, half of them would have decayed and the other half would have stayed. Wait for another 1,600 years, another half would have decayed, and so on and so forth. Now it turns out that if you take elementary particles like muons, they have a half-life of about 1.5 microseconds. We have tested this in labs. But we also get muons in our atmosphere due to cosmic rays colliding with our atmosphere. It turns out that when we looked at these muons, they have a half-life 10 times longer. At first I am like, Einstein, why is that a problem? These are maybe different muons. And Einstein says no. Just like how the charge of an electron stays the same regardless of where the electrons come from, or when you do the experiment, or where you do it, the half-life of a radioactive sample of a particular radioactive isotope would be the same regardless of where that isotope comes from. So how is it possible that these muons would have 10 times more half-life? Well, it turns out that is because they are traveling close to the speed of light. And so if you again plug in the numbers according to special relativity, you get the exact same result: time dilation. Time dilation is literally making these muons age slower. What is physically going on? Something very similar to what we saw in the photon clock. The fact that these muons are moving means that photons are taking a longer, or whatever that force carrier is — photons are not the force carrier, this is a weak nuclear force, but whatever the force carriers are, they will now take a longer time, and therefore the radioactive process gets slowed down. And that is why muons are literally aging slower because they are moving. Time dilation. And if muons can age slower, if radioactive processes can slow down, all biochemical processes can also slow down. And that means living beings will age slower. So if you have two twins — one baby, sorry, two twins, one moving — then you will see the moving twin will age much slower than the twin that is at Earth. This is a real process, and the fact that muons age slower somewhat gives us indirect evidence that this is a real phenomenon. Whoo. And we could still argue that, Einstein, the processes are slowing down over here, and because the force carriers take a longer time because of the motion, but that does not mean that time itself slows down, right? And at this point Einstein says: well, in science you need some process to measure anything, right? And so if you believe that time exists beyond processes and measurements, then it is now beyond the realm of science, and now we are going into philosophical debate, and that is meaningless for science. Science deals with the measurables. So as far as we can measure, everything that is affected by time is being slowed down, and so we say time itself slows down. ### Deriving time dilation with a photon clock Okay, I said, now how does this whole time dilation thing explain why objects can never be accelerated to the speed of light? Einstein says: for that, let’s first derive the expression for this time dilation. At first I am like, no, no, no, I want an intuitive explanation. And Einstein says, do not worry, it will only add to the intuition, and it is also cool to actually derive it because we can do it logically as well. So let’s quickly do that. For that, we are going to use `distance = speed × time`. And if you look at our clock from inside the spaceship, when the clock is at rest, the distance traveled by the photon is just speed into time, so `c × T`. This is the time that we see from inside the ship. Now when we look at it from outside the ship, this is what it would look like, and so if the time taken now is longer, and let’s call that time `T'`, this distance would now again be the speed of light into this new time, the time that we see from outside the ship, `T'`. Now you can see you have two sides of the triangle. If you can figure out the third side, we are done. But what is that third side? The third side is the distance traveled by the mirror in the time `T'`, or the distance traveled by the ship in the time `T'`. And we know the speed of the ship is `v`, then it will become `v × T'`. Now it is just Pythagoras’ theorem. We can use Pythagoras’ theorem to isolate `T'` and figure it out. Great idea for you to pause and derive this historical expression yourself. It is such a proud moment. But if you tried it, here it goes. We will just use Pythagoras’ theorem, and now we are just going to do some algebra to isolate `T'`, and boom, this is the time dilation equation. And let’s pause here because this gives me good BMS. It is one of the cornerstones of physics. And what did we use? Pythagoras’ theorem to derive it. And yet more than 150 years ago, even the smartest folks could not comprehend this. They had no idea that the universe behaved this way. Oh my god. Wow. It can be confusing when we are first learning it, and so Einstein says let’s make sure that we are on the same page with the vocabulary. This `T` is what we call the **proper time**. This is the time that we see when the clock is at rest, and since when things are at rest we see time flowing normally, for us that is why it is called the proper time. Anybody inside the spaceship will basically say nothing weird is happening. The time is proper for me. So, proper time. And this `T'` is what we call the **dilated time**. This is the time that we see when we are looking at things from outside the spaceship. And to make this equation slightly more intuitive, this is how we like to write it. This is the usual notation as well, so let’s familiarize ourselves with this. `γ` is what we call the **Lorentz factor**. We like to talk in terms of `γ` because `γ` is a number that is bigger than one. And again it makes sense: the dilated time must be bigger than the proper time by the factor `γ`. ### How the Lorentz factor changes with speed Now let’s look at some values for `γ` for different values of speed. We can immediately see that even at 50% the speed of light, `γ` is so small: 1.2. So for lower speeds, `γ` is almost 1, and that is the reason why Newtonian physics works. Because if `γ` is almost 1, dilated time is the same as the proper time, and we do not see any discrepancy. We just have one time. But notice, as you go closer and closer to the speed of light, the `γ` value increases. What does it mean? For example, at 87% the speed of light, `γ = 2`. This means the dilated time is twice the proper time. That means when I am looking at the ship in my clock, when 2 seconds tick in that ship, I will see 1 second ticking. It is dilated twice. Similarly, at say 99.9% the speed of light, that `γ` is 22. It means I have to wait 22 seconds for 1 second to tick in that moving clock. Does that make sense? All right, so we have the intuition for where that time dilation comes from because the photon ends up traveling a longer distance. We have the numbers. Now Einstein, it is time to answer the question: why can objects be accelerated to the speed of light? ### Why accelerating a ship gets harder and harder near light speed Einstein says: well, imagine we have a spaceship, a very advanced spaceship, that is accelerating at, say, 1,000 km/s per second. This means that every second that spaceship is gaining a velocity of 1,000 km/s. This will happen if there is a constant force acting on the spaceship. Okay, now initially at very low speeds, we will see nothing weird. We will see every second the spaceship gain 1,000 km/s. So it will start with zero, then it will get 1,000, then 2,000, 3,000. Every second it will keep gaining 1,000, 1,000, 1,000, 1,000, 1,000. But what happens when we go close to the speed of light? Let’s consider 87% of the speed of light. Now from the spaceship’s own perspective, nothing weird is happening because from the spaceship’s own perspective it is still at rest. It will feel the acceleration, just like how we feel the acceleration in the bus. It will feel the acceleration, but the acceleration stays pretty much the same. From the spaceship’s perspective, nothing has changed. It is still spewing out the same amount of fuel. Everything stays the same. But from outside the ship, we will now see that the ship takes 2 seconds to gain 1,000 km/s. In other words, we see its acceleration become half. Why is it happening? Because of time dilation. The whole thing has slowed down. And what causes it? The same effect as before. Because it is traveling so fast, the force carriers are traveling longer distances, so it will take more time for the acceleration to transfer from atom to atom. That is why the whole thing slows down. What happens at 99% the speed of light? We will now see the ship taking 7 seconds to gain an additional 1,000 km/s. You see where we are going with this, says Einstein. The closer we go to the speed of light, the more time it takes for it to gain that 1,000 km/s. Eventually, as we approach closer and closer and closer, it will start taking billions and billions of years to gain additional speed. And therefore you will see that it will take infinite time to actually reach exactly `c`, because the whole thing looks frozen. And again, physically what is going on? When we are going very close to the speed of light, the photons are traveling such a long distance that it is taking them forever to transfer the force from one atom to another. And that is why it is taking forever — literally forever — to accelerate that ship. And that is the reason it takes infinite time. ### Why more fuel does not solve it But wait a second, Einstein. Wait a second, wait a second. What if I were to increase my fuel output? What if I were to increase my fuel proportionately? For example, at 87% the speed of light, what if I double the fuel output? I double my force to get twice the acceleration. Then after time dilation, when you look at it from outside, it will still have the same acceleration as before, right? Einstein says: yes. So let’s do that. Let’s keep up with the time dilation, and let’s keep on increasing the force. But wait, that would mean the faster it goes, to keep up with the time variation and to make sure the acceleration as looked at by us from outside stays the same, they have to increase the fuel output continuously. Oh, that is why it eventually goes to infinity. That is why they would have to use an infinite amount of fuel, infinite amount of energy, because of time dilation, to keep up with the acceleration if they want us to see the same acceleration. Then they have to infinitely, exponentially keep increasing more and more and more and more fuel, more and more force, and that is why it will end up taking infinite energy to accelerate. Ah. So you see what is going on. If you take a finite amount of energy, it will take infinite time. But if you want to do this in finite time, it will take infinite energy. Does it all make sense now? And it is all because of that one thing: the speed of light stays constant in all reference frames. And therefore, as you go faster and faster, photons will take forever to transfer energy, to transfer forces, and that is the reason why nothing ever can accelerate to the speed of light. Wooo. ### The deeper takeaway So now I hope you have a complete intuitive idea of why nothing can ever be accelerated close to the speed of light. It is all because of time dilation, which stems from the fact that the speed of light is always constant in all reference frames. And what is beautiful is that every single thing in relativity, whether it is Lorentz equations, solving the twins paradox, or even deriving `E = mc^2`, which we will do next, by the way — all of that can be done intuitively just from that one postulate. And that, I find, is truly, truly mindboggling. I will see you soon.