VIDEO TRANSCRIPTION
FloatHeadPhysics
I never understood why you can't go faster than light - until now!
Description generated by Skrybot
The explanation provided delves into the concept of time dilation and its implications on accelerating objects to the speed of light. It highlights how as objects approach the speed of light, time dilation causes their acceleration to slow down significantly, ultimately requiring infinite energy to reach the speed of light. This phenomenon is rooted in the constant nature of the speed of light in all reference frames. The discussion also emphasizes the intuitive understanding of complex physics concepts through the lens of time dilation.
Transcription generated by Skrybot
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 got is if you take the graph of the kinetic energy versus the speed. Look, as the speed approaches c, kinetic energy goes to infinity so it takes infinite energy. But my problem is that that's not an explanation. I don't have an intuition behind why that is true. Another explanation was mass goes to infinity but again there is no evidence for that. So what's really going on? What's the physically. . . happening that's limiting that ship from going towards the speed of light. That's what we're going to try and answer in this video.
And so if you're ready for it, let's begin. So Einstein, where do we start? Einstein says, imagine you are inside a very fast moving ship and you have a photon clock with you. Now at this point, I say, wait a second, Einstein, I don't want to deal with hypothetical clocks. I want to talk about real clocks. Einstein says, well, buddy, patience. If you understand photon clocks, you'll be able to understand everything else. I'm like, okay, cool. Let's trust him. So what's a photon clock? It's a clock where you have two mirrors and photon bounces between the two and we can say that hey when the photon hits the bottom mirror it hits a tick.
So we get tick, tick, tick, tick, tick and so on and so forth. Now Einstein asks what would the same clock look like if you are seeing the whole thing from outside the ship. Well, let's see. At first I'm 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 the photon is now traveling a diagonal path. This means it's going to travel a longer distance. But remember, the photon always travels with the speed of light. See, the speed of light is the same in all reference frames, which means the photon now is going to take a longer time between the ticks.
In other words, we will see that photon clock tick slower. So again, let's compare. Here's what the photon clock would look like from inside the ship. Look at the ticks. Tick, tick, tick, tick. Now 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 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.
Now at this point I say, cool, photon clocks tick slower, that's great, but what about real physical clocks, Einstein? Well Einstein says if you look at this clock and if you 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 ticking like this then the animation would look something like this. But Einstein says that can't happen. You can't have something like this. And the reason is when say this atom accelerates, this atom particular 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 the other atom can 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 you see, the whole thing is not instantly going, but it's so fast that it feels like it's instantly going.
But now Einstein asks, Mahesh, what if now this set of atoms were moving? What would the animation look like now? Wait a second, this also is 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. Well, let's look at it, 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're moving. Whoa.
But at this point, we can ask Einstein, is there evidence for this? This is just a theory, right? So Einstein says, well, probably not in his time, but today we do. You see, we've actually 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 and every time we checked, we saw that the amount they went out of saying perfectly predicts is perfectly predicted by special relativity. Now of course gravity also affects it which is dealt in general relativity. So there is this additional effect that's 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 the time itself is slowing down, Einstein? Einstein says for that, let's look at radioactivity. 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 particular radium isotope, it has a half-life of about 1600 years, which means that if you take a billion radium isotopes, wait for a 1600 years half of them would have decayed and the rest half would have stayed. Wait for another 1600 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 one and a half microseconds. We did that in lab. We have tested this in labs but we also get muons in our atmosphere due to the cosmic rays colliding with our atmosphere. Turns out that these muons when we looked at them they have a half-life of 10 times more. At first I'm like Einstein, why is that a problem? Like 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 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, turns out that's because they're traveling close to 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. But what's physically going on? Something very similar to what we saw in the photon clock. The fact that these muons are moving, this means that photons are taking longer.
Or whatever that force carrier. 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's why muons are literally aging slower because they're moving. Time dilation. And if muons can age slower, if radioactivity process 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's at Earth. This is a real process. And the fact that muons age slower somewhat gives us an indirect evidence.
that this is a real real phenomenon.
Whoa! 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 doesn't mean that the time itself slows down, right? And at this point Einstein says, well Mahesh, in science you need some process to measure anything, right? And so if you believe that time exists beyond the processes and measurements, then it's now beyond the realm of science and now we are going into philosophical debate and that's meaningless for science so science deals with the measurables and 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 okay Einstein now how does this whole time dilation thing explain why objects can never be accelerated to speed of light Einstein says for that let's first derive the expression for this time dilation and at first I'm like no no I want an intuitive explanation and Einstein says don't worry only add to the intuition.
And it's also cool to actually derive it because we can do it logically as well. So let's quickly do that. So for that, we're going to use distance equals speed over time. And if you look at our clock from inside the space, when the inside the spaceship, when the clock is at rest, the distance traveled by the photon is just speed into time. So c into t. So 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 as t dash, this distance would now again be the speed of light into this new time, the time that we see from outside the ship, t dash. And 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 dash, or the distance traveled by the ship in the time t dash, and we know the speed of the ship is v, then it'll become v times t dash.
And now it's just the Pythagoras theorem! We can use Pythagoras theorem to isolate t dash and we can figure it out. Great idea for you to pause and derive this historical expression yourself. It's such a proud moment. But if you've tried it, here it goes. So we'll just use Pythagoras theorem. And now we're just going to do some algebra to isolate t dash. And boom! This is the time dilation equation. And let's pause here because this gives me goosebumps. It's 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 couldn't 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's why it's 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 dash 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. Gamma is what we call the Lorentz factor. And we like to talk in terms of gamma because gamma is a number that's bigger than one. And again, it makes sense. The dilated time must be bigger than the proper time by the factor gamma. And now let's look at what are some values for gamma for different values of speed. So let's do that. And you can immediately see even at 50% the speed of light, gamma is so small, 1. 2. And so for lower speeds, gamma is almost 1.
And that's the reason why Newtonian physics works, because if gamma is almost 1, the dilated time is the same as the proper time, and we don't see any discrepancy, we just have one time. But notice as you go closer and closer to the speed of light, gamma value increases. What does it mean? So for example, at 87% the speed of light, gamma is 2. This means the dilated time is twice the proper time. That means when I'm looking at the ship, in my clock, when two seconds tick, in that ship I will see one second ticking. It's dilated twice. Similarly, I'd say 99. 9% the speed of light, that comma is 22.
It means I have to wait 22 seconds for one second to tick in that moving clock. Does that make sense? Alright, so we have the intuition for where that where the time dilation comes from because the photon ends up traveling a longer distance. We have the numbers now. Einstein, it's time to answer the question why can't objects be accelerated? to the speed of light. So Einstein says well imagine we have a spaceship very advanced spaceship that is accelerating at say thousand kilometers per second per second. This means that every second that spaceship is gaining a velocity of thousand kilometers per second. This will happen if there's 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 a thousand kilometers per second. So it'll start with zero, then it'll get thousand, then it'll get two thousand, three thousand. Every second it'll keep gaining thousand, thousand, thousand, thousand, thousand. 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'll feel the acceleration, just like how we feel the acceleration in the bus. It'll 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 two seconds to gain 1000 kilometers per second. 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? Well, the same effect as before. Because it's traveling so fast. The force carriers are traveling longer distances, so it will take more time for the acceleration to transfer from the atoms to atoms. That's why the whole thing slows down. What happens at 99%, say the speed of light? We will now see the ship taking 7 seconds to gain additional 1000 km per second.
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 1000 km per second. Eventually, as we approach closer and closer and closer, it'll 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's going on when we are going very close to the speed of light? See the photons, they're traveling such a long distance that it's taking them forever.
to transfer the force from one atom to another and that's why it's taking forever literally forever to accelerate that ship and that's the reason it takes infinite time but wait a second Einstein wait a second wait a second what if I were to increase my fuel output 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 dilation and to make sure the acceleration as looked by us from outside stays the same, they have to increase the fuel output continuously. Oh that's why it eventually goes to infinity. That's why they would have to use infinite amount of fuel, infinite amount of energy because of time dilation to keep up with the acceleration. If you 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's why it'll end up taking infinite energy to accelerate. Ah, so you see what's going on? If you take finite amount of energy, it'll take infinite time.
But if you want to do this in finite time, it'll take infinite energy. Does it all make sense now? And it's all because of that one thing. That speed of light stays a 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's the reason why nothing ever can accelerate to speed of light. Whoa! Whoa! So now I hope you have complete intuitive idea of why nothing can ever be accelerated close to speed of light. It's all because of time dilation which stems from the fact that speed of light is always a constant in all reference frames.
And what is beautiful is that every single thing in relativity, whether it's Lorentz equations, solving the twins paradox, or even deriving E equals mc squared, 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 mind-boggling. I'll see you soon. .
S K R Y B O T
Skrybot. 2023, Video transcriptions from YouTube
By visiting or using our website, you agree that our website or the websites of our partners may use cookies to store information for the purpose of delivering better, faster, and more secure services, as well as for marketing purposes.