I Never Understood Why Black Holes Slow Down Time… Until Now!

this video is sponsored by brilliant.org do you remember that scene in the movie Interstellar where bran and Cooper decide to explore a planet very close to a black hole to see if it's habitable but after a few hours just few hours they realize it's not so they turn back and even though they come back in a few hours a lot of years would have passed for their friend ROM whom they left behind so from their perspective the whole trip took only a few hours but from his perspective he waited for years how many years you

ask well 23 years 4 months 8 days and it's not just him everyone on Earth including his daughter Murphy would have aged a lot so the big question is why did this happen well the most common explanation explanation I should say that I got is that gravity slows down time and therefore the time very close to a black hole takes much slower passes much slower compared to far away and that's why they did not age much but guess what that's not an explanation you said the same thing just just by using the words gravity and

time now it's kind of like saying um apple is red because Apple emits red color that's not an explanation so for a long time I thought I wouldn't get any intuition behind what's really going on over here until I read this book by the author surprise surprise Albert Einstein the book is called relativity the special and general theory it's a very thin book and there is a section in this in which Einstein describes a beautiful way to think about this which definitely give me a lot of intuition and so I want to share that with

you so if you're ready to understand what really happened over here um instead of just saying gravity slows down time well let's begin so where do we start well Einstein asks mes what is gravity exactly well I say you know gravity is the force of attraction between any two masses it's the force that the Earth puts on us because of which the Apple accelerates down and it's also the force because of which I feel my own weight and Einstein says cute very cute is but that is a Newtonian model and in this model obviously you

will not get any intuition for why clocks slow down close to the planet but remember according to Einstein's model there is no force of gravity at all nothing is pulling down on us then why does the apple fall down why do we feel our weight well that's because Einstein says it's the ground that is instead accelerating up to meet the apple and just like how when you are in a bus that suddenly accelerates forward you feel a backward jolt a jolt in the opposite direction dire similarly on this accelerating ground we feel a downward jolt

a jolt in the opposite direction which we think of it as gravity but it's a fictious Force so in Ein science model gravity is an artifact of being in an accelerated frame and guess what in an accelerated frame like this clocks will take at different rates but wait a second wait a second we're getting ahead of ourselves at this point immediately a question that should come to our mind is Einstein if the ground is accelerating up up and Earth is round shouldn't the same thing happening on the other side as well which means these two

patches of Earth should be moving away from each other so the Earth must be expanding but clearly the Earth doesn't expand so I call this explanation baloney and I says here we go again all right Mahesh for a second completely forget whatever I just said and instead imagine we are in deep Intergalactic space where there's no gravity no planets nothing let's say we just have these two patches of you know ground accelerating towards each other what's going to happen to them well I say well if you accelerate them towards each other like say by putting

Rockets well they'll eventually bump into each other right like Lon says of course that would be the case if you use Rockets to accelerate them but there's another way to do that what if we attach them to a ring and make it spin okay what happens when you make it spin well iand reminds us that when something is rotating they they experience a centripetal acceleration an acceleration towards the center so both of them are accelerating towards the center and yet look the distance between them is not decreasing the they're not coming closer to each other

and I'm like okay all right let's look at it a little bit more closely at this point everything over here is moving to the right so if you were to drop an apple then that Apple would also have a velocity to the right and so if you drop it it will continue moving to the right with a constant velocity because remember there are no forces over here there's no gravity there's no planets there's nothing right so if you let go of a an apple it should go to the right but at the same time this

whole patch of space and this whole patch of ground curves upwards so see what happens as the Apple goes to the right eventually it'll be blocked by the ground and so notice from her perspective it just feels like the Apple fell down but notice the Apple did not accelerate the apple is just following its straight line inertial path Newton's first law it is the ground that accelerated up to meet the apple and the same thing is happening with her as well because of her inertia she also wants to travel straight to the right but because

the ground is accelerating up it's the ground that's pushing her up and deviating her from her straight line path so clearly you can see it's the ground that's accelerating her up towards the center and as a result if there was a weighing skill over here that weighing skill would get pressed and as a result she will feel her own weight so they will feel all the effects of gravity even though it's not there so if you were to zoom out a little bit just like how when a car takes a turn we experience an outward

push a centrifugal force we call it it's not that's not real in a similar way look they're all the both of them are experiencing an outward push which they will attribute as gravity so we have simulated Gravity by accelerating them towards each other and look in that accelerated frame they are at rest remember from their own perspective they are at rest with respect to each other and it's the rest of the universe that's moving so look there we have it so if these were Newton they would say that hey there is gravitational force acting down

here and there's a gravitational force acting down here and if these are Einstein they say uhuh it's an artifact of our ground accelerating up and yet the two pieces of ground are not moving towards each other it's possible so Einstein now says okay Mahesh this means it's possible to have two pieces of ground accelerating towards each other without moving towards each other like we seeing over here now if that is possible can't you be open to the possibility that it's possible that two pieces of ground can accelerate away from each other without moving away from

each other don't you think that's possible possible at least can you be open to that possibility and I'm like yeah now that you put it that way maybe it's possible but how over there it's the spin that makes it possible over here what makes it possible well lense says it's a slightly more complicated over here turns out it took him a lot of time to figure this out but turns out the SpaceTime itself is curved that curvature allows it to happen now I know calling SpaceTime curvature doesn't help and doesn't explain anything but we have

made a detailed video on this where we talked about this and we built models and whatnot to to understand this in great detail but I'm going to link on to it but don't click on it I don't want you to click on it right now because let's not get distracted from it so coming back over here if you were to summarize what we just learned from Einstein's perspective there is no force of gravity it's an artifact of the ground that's just accelerating up and even though ground is accelerating up there's a way to conceptualize this

without Earth having to expand okay now here's the thing just like how gravity is an artifact of this acceleration there's another artifact and that is is the time or clocks will take differently time will pass at different rates but how how does time pass a more quickly at a height because of acceleration well lense says that's kind of like how mahes time passes for you very quickly when you're completely immersed using brilliant.org the sponsor of this video I'm super glad that you watch my videos thank you for doing that but to be honest if you

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the description as well of course through this link you'll also get a 20% off on your annual subscription so do check them out I've been recommending them to my students from way before they started sponsoring me so do check it out all right back to the video okay seriously now why is it that in an accelerated frame clocks take at different rates time passes at different rates at different heights well for that Einstein says think about a rotating disc and I'm like come on rotating disc that's so mundan give me something more interesting something more

and I says all right mahes how about rotating intercell spaceship and I'm like that's what we are talking about rotations have an interesting property if you were to concentrate at different points that are different distances from the center notice as this as this ship rotates the points which are very close to the center hardly move look at this this velocity is very low it's hardly moving but the points that are very far away oh my God my cursor I can't even keep it up oh my God it's moving so fast but this one look at

that oh my God it's moving so slowly oh nothing oh my God look at that oh wow that's moving so fast so points that are far away farther you go from the center they move faster and faster and faster and why should I care about this Einstein well Einstein says M remember time dation in special relativity moving clocks take slower compared to the clocks that are at rest and an intuitive way to think about it is in terms of photon clocks if you have a photon clock with you at rest it'll keep ticking at the

maximum speed but if the same clock is moving now the light has to travel a biger distances between the ticks and since its speed is the same in all reference frame it takes more time to tick it slows down and if it's moving even faster time slows down even more there's nothing new over here we've learned all of this in special relativity normal time dilation when things move okay but now we can apply it over here okay remember we are outside we are looking at this from far away we can you can imagine we are

at rest with respect to the center of this spaceship okay now from our perspective look people over here are hardly moving they're pretty much at rest they're hardly moving so their clocks are not dilated at all their clocks are taking pretty much at the same rate as our clock but look at the people over here oh my God because they're moving so fast much faster than people over here their clocks will be dilated a lot more and therefore their clocks will be ticking much slower than our clocks so as we go farther and farther away

the clocks sck slower and slower again nothing mysterious over here that's all because they have different speeds everything makes sense from our perspective but now comes an important question what does it all look like from their perspective for people inside this spaceship here's the way to think about it imagine the people over here they all were of the same age before they got into the spaceship okay so now we know that the person over here would have aged the least because their time ticked the slowest and the person over here aged the most therefore when

they meet up what should happen they should all agree on that age right regardless of whose perspective we think about it when people meet up everyone should agree on who ages more and who ages who who ages less so it's an objective fact doesn't matter who looks at it but the second thing to understand is that remember people never see themselves aging slower okay I will always regardless of where I am on the ship I will always see my clock ticking nor normally and I will see me me myself aging at the same rate and

so putting this these two together we can Now understand what they will see you know inside the spaceship so if if you go inside the spaceship the person at the bottom will say hey my clock is sticking normally but if they could somehow look at the person at the top they will say oh my God you are aging so fast and of course there will be some light abberations and all of that but don't worry about it for now um but they will eventually infer that oh my God that person is aging so quickly on

the other hand the person over here says uh-uh I am aging normally buddy it's you who's aging very slowly that's what they will all infer but here is the most interesting question why are the clocks Die Why are different people aging differently from the perspective of the ship from the perspective of the ship look everybody is at rest nobody's moving from our outside's perspective we had a simple answer special relativity time dilation but what's the answer from inside the spaceship they're all wondering what's going on over here why are we all aging differently because we

are all at rest relative to each other look they're all at rest it has to be gravity they will all infer that this must be due to gravity why why do they infer that it's due to gravity we'll think about it this way if we had a remote control we who are standing far away from this ship from outside the ship if we could somehow switch off the rotation then of course all of their clocks will now start ticking at the same rate because nobody's moving and therefore from inside the spaceship they will suddenly see

hey gravity has switched off and now they will see oh my God all of us are now ticking at the same rate oh and when you switch on the rotation again gravity gets switched on and now look oh my God okay clocks now again start ticking at different rate so the only thing that's making clock take a different rate they will infer is gravity fictious Gravity from inside this is how gravity and clock ticking is connected to each other so if you put it all together being in an accelerated frame gives you two effects one

it gives you the illusion of gravity and two now that we seeing it is that it makes clock stick at different rates at different locations okay Einstein let's bring it home let's now answer our original question and says we need one last thing if you look at this from the outside perspective one more time remember because people over here are traveling very slowly the acceleration that they feel would be very small and the people over here are traveling very fast so the acceleration that they feel would be very large this means from inside the spaceship

if you look at people who are over here because they have very small acceleration they will say that hey they feel very small gravity but if you go very far away over here they will say that oh my God the gravity over here is much larger which means this means the apparent gravity that they all feel that becomes bigger and bigger as they go farther and farther away and if you connect it to the time the clocks now you can see that means the lower you go in the gravitational field the slower the clock takes

this now explains why closer to the surface of any planet or the star the clocks will take much slower so being over here where you experience the maximum gravity it's kind kind of like being on the surface of the planet and being at the center which is where you feel almost no gravity is like being infinitely far away from the planet so it's a great model but of course it's a rough model the gravitational field does not increase in the same way the gravitational field increases over here so don't don't look too much into the

model but it gives you gives us brilliant intuition now explaining why the clocks must be dilated closer you know closer to the surface of the planet compared to clocks that are farther away now if we are modeling Earth since the gravitational acceleration is very tiny near the surface of the Earth that means we need we don't need a lot of velocities over here the people inside will be moving at a very low velocity compared to us where we are you know we are standing outside of this okay at such low velocities the time dilation is

hardly anything so we don't need special relativity and our clocks pretty much take at the same rate that's why when you're dealing with regular planets or Stars we can use Newtonian model and completely forget time dilation but if you're close to a black hole the fields that we're dealing with over here are insanely High which means if you want to model that over here using our spinning space station we need a huge space station and we need to spin it very fast so that people over here are pretty much traveling close to the speed of

light as seen from us from the outside and people over here will not be traveling much at all that means the clock discrepancy will be severe the clocks over here will be hardly ticking this is the reason for the severe time dilation in our model we can think that bran and Cooper were somewhere over here traveling pretty close to speed of light from our inertial perspective so their clocks didn't tick much at all romaly on the other hand was pretty close to the center over here and therefore his clock is sticking pretty much at the

same rate as our clock so not much dilated at all and therefore we had to wait a lot of time for them like years decades actually for them to come back over here so what blows my mind away is that it all boils down to the fact that the speed of light is a constant in every reference frame that's where we got the time d to begin with and that's why in accelerated frames also clocks should be dilated I find that I find that really incredible so do you now have a better intuition for what

happened in the interstellar scene can you now explain to somebody better than just saying gravity slows down time if you can I want you to do me a favor no no no don't like share subscribe I don't care about any of that but instead in fact instead of sharing this video instead you try and explain it to them yourself just do that right away it's because when you're trying to explain it to somebody that's when you will understand the gaps in your explanation and that's when you'll be learning a lot more I'm sure I had

a lot of gaps over here and I definitely learned a lot more than when I just started making this video so yeah do that that's called The Fan technique and that's one of the best ways to learn right that's all I got yeah that's all I got all right see you bye-bye