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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.

• 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.

• 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.

B2 中高級 美國腔

什麼是奇點？| 永恆的好奇#11 (What is a Singularity? | Eternally Curious #11)

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