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  • Hi, my name is Fede and this Eternally Curious.

  • What’s a Singularity?

  • Well we say someone is singular when they areone.

  • A single person.

  • And not just any individual, someone odd.

  • But that’s not quite right.

  • A singularity is more like the answer to a question for which there is no answer.

  • Confusing?

  • Here.

  • Take this very simple function.

  • When x is 1, what’s the value of f(x)?

  • OK, let’s substitute.

  • 1 over 1 is… 1.

  • Now what happens when x is zero?

  • Well that’s easy.

  • Substitute, and

  • The function has no solution, because it doesn’t make any sense,

  • because 1 divided by 0 doesn’t make any sense.

  • Unless you use a Riemann sphere in the complex plane which allows for division by zero in

  • some circumstances, in a way that makes expressions such as this one well-behaved.

  • The point is that these are just constructs.

  • They don’t exist in the real world.

  • They are more like ideas.

  • See, when we built mathematics, we decided the rules, and according to those rules this

  • equation doesn’t make any sense.

  • It has no answer.

  • So what’s the problem?

  • It all goes backs to this guy.

  • Einstein’s field equations.

  • You can easily derive their exact solution

  • for a single spherical non-rotating mass if your name is Karl Schwarzschild and youre

  • a genius physicist with a badass mustache

  • and then you end up with this, simple-looking formula.

  • Let’s unpack this.

  • c is the speed of light G is the gravitational constant

  • M is the mass of the object and rs is the Schwarzschild radius

  • c and G are constants.

  • Say you have an ball of mass M.

  • If you squeeze it, the mass stays the same but its volume gets smaller.

  • If you keep squeezing the ball, it will become tiny, but stay just as massive as before,

  • all the molecules compressed close to each other.

  • Until it reaches a critical size.

  • And that’s the Schwarzschild radius.

  • It is the radius of a sphere such that, if all the mass of an object were to be compressed

  • within that sphere, the escape velocity from the surface of the sphere would equal the

  • speed of light.

  • This means that in order to escape the gravitational pull of the object, whatever tries to get

  • away from it would have to move faster than the speed of light.

  • But because the speed of light is constant and nothing can ever go faster, nothing can

  • escape.

  • Including light.

  • It’s essentially a black pit where anything you put in doesn’t come back.

  • And that’s what we call the congressional budget.

  • I mean, a black hole.

  • Because the speed of light is such a gargantuan number.

  • Its square is f**king gianormous.

  • Which means unless you have an unbelievably big mass, the Schwarzschild radius is very

  • tiny.

  • Take the Earth, which is pretty massive.

  • It has a radius of over 6,000 km.

  • Its Schwarzschild radius is only 8mm.

  • I don’t think I can even begin to explain the scale of things.

  • It would be like turning this gigantic thing where all of humanity lives cozily and people

  • take years to travel around by foot.

  • Into something the size of a penny.

  • Let’s go back to our Schwarzschild radius.

  • If the object’s radius is less than that, it becomes a black hole.

  • But what happens at the center?

  • In other words, what happens if the object's radius IS zero?

  • This equation defines the shape of spacetime near a spherical mass.

  • Now you don’t need to understand all of it.

  • Just have a quick look and see if you can spot the problem.

  • Congratulations, you just broke physics.

  • By creating a singularity.

  • An imaginary point in spacetime where all the laws we know don’t make any sense.

  • Now let’s make something clear.

  • The black hole isn’t the singularity.

  • This is the event horizon, sort of a “beyond this none shall returnthreshold.

  • That’s the black hole.

  • And in the middle it's where you divided by zero.

  • The singularity isn’t really a place, because in theory it occupies no space, and it has

  • infinite density.

  • It’s like the concept of point in geometry.

  • It’s hypothetical.

  • Except we have experimentally discovered black holes, exactly how Einstein and Schwarzschild

  • had predicted, and there is reason to believe that singularities do exists.

  • There is copious amount of speculation on what might happen at a singularity, including

  • wormholes, time travel, and portals to other universes.

  • If youre curious about that please let me know in the comments.

  • We just don’t know for sure what happens at a singularity, and probably never will.

  • At least not until we get toTHE SINGULARITY”, which I’ll explain in a later video.

  • But only if you click this button here to subscribe.

  • Check out my other Eternally Curious videos here.

  • And if you really like what I do you can support me on Patreon here.

  • Thank you for being curious.

Hi, my name is Fede and this Eternally Curious.

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シンギュラリティとは何か?| 永遠の好奇心 #11 (What is a Singularity? | Eternally Curious #11)

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    gotony5614.me97 に公開 2021 年 01 月 14 日
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