"I never understood why you can't go faster than light - until now!" - Transcript | YTScribe

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's 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 flight that's what we want 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 where is 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 shape 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 that 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 TI 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 photons clock Photon clocks take 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 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 can't happen you can't have something like this and the reason is when say this atom accelerates this atom particular accelerates the 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 mahes what if now the 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 oh 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 part just like before and therefore real physical clocks actually slow down look at this this one is sticking slower than this one real physical clocks slow down when they're moving wa

but at this point we going as 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 sying perfectly predict is is perfectly predicted by special relativity now

of course gravity also affects it which is De dealt in general relativity so there's 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 DK is where you have an unstable atom that spontaneously splits the cool thing about radioactivity is that they

have something called the halflife for example if you take a radioactive is radium particular radium isotope it has a half lifee about, 1600 years which means that if you take a billion radioactive radium Isotopes wait for 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 1 and a half micros seconds 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 halflife 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 it'll or when you do the experiment or where you do it the half lifee of radioactive sample of a particular radioactive

isotope would be the same regardless of where that isotope comes from so how does how is it possible that these muons would have 10 times more halflife 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 AG 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 a

longer or whatever that Force carrier phons 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 slow down and that's why muons are literally aging slower because they're moving time dilation and if muons can age slower if radioactiva 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 ate slower somwhat 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 mahes 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 I said now how does this whole time dilation thing explain why objects can never be accelerated to speed of light I said say for that let's first derive the expression for this time dilation and at first I'm like no no

no I want an intuitive explanation and Einstein says don't worry it will 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 equal speed over time and if you look at our clock from inside the space when the inside the space shape 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

shape 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're done but what is that third side the third side is a distance traveled by the mirror in the

time T Dash or the distance Trav by the ship in the time T Dash and we know the speed of the ship is V then it will become V * T Das and now it's just a Pythagoras Theorem we can use Pythagoras Theorem to isolate t- and we can figure it out great idea to for you to pause and derive this historical expression yourself it's such a proud moment um 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 Das

and boom this is the time dilation equation and let's pause here because this gives me good BMS 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 Universe behaved this way oh my god wow it can be confusing when we are First Learning first learning it and so Einstein says let's make sure that we 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're looking at things from outside the space shap 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 Lawrence factor and we like to talk in terms of gamma because G GMA is a number that's bigger than one and again it makes sense the tiated 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 one and that's the reason why Newtonian physics works because if gamma is almost one dileted 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 2 seconds stick in that ship I will see 1

second ticking it's dilated twice similarly at say 99.9% the speed of flight that comma is 22 it means I have to wait 22 seconds for 1 second to take in that moving clock does that make sense all right 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 th000 km/s per second this means that every second that spaceship is gaining a velocity of 1000 km/s 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 1,000 km/ second so it'll start with zero then it'll get th then it'll get 2,000 3,000 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 that's 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'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 2 seconds to gain th000 km/ second in other words we see it 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'll 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 flight we will now see the ship taking 7 seconds to gain additional 1,000 km/ second you see where we going with this says Einstein the closer we go to the speed of flight the more

time it takes for it to gain that th000 km/s 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 exelate 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 varation 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 ex if 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 will 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 frame 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 W wo 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's beautiful is that every single thing in relativity whether it's lowen equations solving the twins Paradox or even deriving equals mc² which we'll 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'll see you soon e