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Impossible Numbers


"Gather ye rosebuds while ye may, Old Time is still a-flying, And this same flower that smiles today, Tomorrow will be dying."

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Nov
13th
2022

Black Holes, or The Abominations of Reality · 3:54pm Nov 13th, 2022

Did you know that anything could be turned into a black hole? For every object with mass, there's what's called a Schwartzchild radius: compress the object to below that radius, and bam! Black hole singularity.

Every object.


Blog Number 205: Schwartzchild Radius Edition

For instance, if you wanted to turn the Sun into a black hole, you'd need to compress it to a radius of approximately 3km, or narrower than Manhattan is wide. For Earth? Approximately 1cm, or the size of a grain of rice.

A human? Roughly a hundred-millionth the size of a subatomic particle like a proton.

Now you've got some idea of what kind of immense force it takes to turn a supergiant star a million times bigger than our Sun into a black hole that's merely five times wider than said Sun.


Fortunately, the chances of this happening to you are nonexistent.

In fact, the main reason the vast majority of objects you can think of don't compress into black holes is because black holes are gravitational extremes, and it usually requires at least three solar masses emerging from a high-energy supernova implosion-explosion to trigger a runaway gravitational collapse. No human technology could possibly generate the required level of force. Even Nature needs special conditions in order to do so.

And while Bill's in the time-out corner, here are a bunch of pretty artistic impressions of black holes, for absolutely no reason.

Bill Cipher may be fiction, but eldritch abominations are real.
Source: https://www.space.com/15421-black-holes-facts-formation-discovery-sdcmp.html


Firstly, you need a lot of mass. Matter in a finite volume generally attracts more matter within its gravitational radius. Did I mention that gravitational radius is basically infinite? Everything has a gravitational pull on everything else.

The secret to why we don't all collapse into an instant big crunch is that gravity is weak as all get-out.

In space, accreted objects are not stationary clumps - which, given time, would eventually be drawn together into bigger and bigger clumps - but are constantly thwarting gravity by the simple expedient of... moving.

Using energy to counter it, in other words. As a result, they're barely affected. Even whole galaxies are mostly moving away from each other, though that brings us into the realm of dark energy and possibly inflation, esoteric topics which aren't necessary for much of what I'm about to say.

True: some matter will be moving in the right direction, bringing them close enough to compactify. But that's actually a rare thing relative to how much stuff there is in the universe.

Most objects are moving fast enough that they simply end up in various kinds of orbit. Others end up swinging themselves out of orbiting range (thus their kinetic energy - motion energy - ends up weakening the pull of gravity the further away they get), or simply move too relatively fast to be deflected much in the first place.

See, compactification in the first place requires anisotropy, such as an already-compact amount of matter in a nebula to begin working with gravity rather than against it, collapsing into tiny asteroids, medium-sized planets, Sun-like stars, or even supermassive stars.

Naturally, that anisotropy (local imbalance in e.g. matter distribution) is going to run out of its local supply eventually, and not much is going to be coincidentally on a collision course with it to add any further significant mass.

Surprising as it may seem - given we need expensive rockets to reach escape velocity (i.e. constantly generate enough upward force to leap into non-friction-impeded orbital or post-orbital range) - but kinetic energy can actually overcome gravity surprisingly easily, otherwise we wouldn't be able to pick up objects against the combined gravitational force of the planet with our noodly little arms.

Even this guy's stronger than gravity.


Hence why you need a massive amount of concentrated mass to overcome that kind of easy-peasy counter.

Once concentrated, though, that's it, right? Kinetic energy, for instance, doesn't mean much if there are atoms everywhere you go, all gravitationally attracting each other from all directions. So black hole time, right?

Well, no. Even in their trapped state, atoms obey the forces governing the interactions of subatomic particles and discrete energy packets (quanta, from which "quantum" is derived). Those forces govern all our complex interactions, from chemical processes and how light moves to what makes atoms atoms in the first place. Such forces are much stronger than gravity, and so in turn it requires a lot of gravity (in practical terms, a lot of mass) even to begin to overcome them.

What prevents trigger-happy black hole formation from happening in any old star is a combination of these opposing forces. The most obvious is the electromagnetic force, which is what normally prevents atoms from doing more than collide anyway. When you touch something, for example, what's really going on is that the electromagnetic force fields of your atoms repel the electromagnetic force fields of the object's atoms.

This force is also responsible for chemical processes, because the movement of electrons (the electromagnetic force-carrier particle) and their absorption or emission of energy determines how two substances will combine or break apart. It's basically the force that keeps your molecules together, it's therefore responsible for the larger-scale interactions of your body parts, and it's ultimately what makes you you.

You'd need a nuclear fusion reactor to overcome that, and human researchers are still struggling to make one that doesn't fizzle out instantly.

Speaking of which, the nuclear fusion of the star itself also counters the runaway collapse of gravity. Even though nuclear fusion overcomes the electromagnetic force if enough kinetic energy is active (i.e. the atomic nuclei smash into each other really hard), the same condition also means that the strong nuclear force kicks in, binding nuclei together but keeping them locked together according to quantum theory.

This is essentially what makes stars such good generators of higher elements: they literally fuse them out of the nuclei of smaller elements, hence "nuclear" and "fusion".

So no worries about the first working nuclear fusion reactor running away and making a black hole, people.

"Yeah, right. Just don't come crying to my fallout shelter when it all goes belly-up, you jerk, cos you ain't gonna be on the guest list."


Therefore, even most stars - gravitational hotspots - won't instantly turn into black holes.

However, this only lasts as long as the nuclear fusion in the star does. Once it runs out of fuel (typically hydrogen and helium, the lightest elements and therefore easiest to fuse), then the star is subject to its own degeneracy pressure in what I shall wilfully personify as a "last-ditch" move to prevent total collapse.

Those stars whose core is lighter than 1.4 solar masses simply eject their outer layers as planetary nebulae and become white dwarfs, in which electromagnetic particles (electrons) define the degeneracy pressure that pushes outward and resists gravitational collapse. White dwarfs eventually fizzle out and become black dwarfs, little better than dense planets.

Those whose core is heavier than 1.4 solar masses become neutron stars, in which it is the neutrons in the nuclei which define the degeneracy pressure. But note that neutron stars are also the result of a supernova detonation, meaning the outer layers collapse (implode), hit the core, rebound, are ejected at impossible speeds, and in so doing generate a breathtaking amount of energy (explode). Most of the mass will thus be lost, so the fate of the original star ultimately depends on how much mass the resultant star contains. Neutron stars require a resultant mass of between 0.1 and 3 solar masses.

Any higher, and something else happens. The imploding energy is so great that gravity overcomes any other possible fundamental force. Meaning it crushes the mass so strongly that it breaches the elusive Schwartzchild radius.

From this point on, nothing can escape the gravitational collapse, not even pure energy at the cosmic speed limit (i.e. light). With no further opposition, gravity collapses the mass into an infinitely dense singularity surrounded by an event horizon. A black hole.


"Wow. The universe is so... breaky..."


So basically, black holes can only be made by extremely and painfully violating the normal laws of the universe, to the point that their existence is actually where the laws of Einsteinian general relativity - i.e. the laws that govern our universe - break down. They don't even have an agreed-upon quantum explanation yet, simply because gravity is such an oddity within the Standard Model of particle physics.

Well, that's reassuring, isn't it?

To get back to the original point:

In order for you to turn into a black hole, you'd have to be compressed hard enough so that the atoms inside you can no longer repel each other, compressed hard enough that even the fused nuclei can no longer repel each other, possibly violently slough off most of your outer layers to generate even more collapsing kinetic energy, and basically implode-explode yourself (and therefore blast anyone unlucky enough to be standing on the same planet as you) to a pinprick smaller than a hundred-millionth of a proton.

And that's never gonna happen, of course.

"Hmm. It's a million-to-one chance, but it's just crazy enough to be funny..."


Worse, have you heard of supermassive black holes? They are monsters even by black hole standards (in fact, the common understanding of a black hole is the stellar black hole: yes, there's more than one type!). And they sit at the cores of most galaxies, not as anomalies but apparently as a normal feature.

By the way, you think we're exempt? Then I advise you not to look up Sagittarius A* (no, it's not a grade on the constellation's report card, hahaha) in the dark journals of the Stellanecronomicon (i.e. any astronomy text). It might just blow your mind.

And that's before I float the possibility of primordial black holes, yet another (if much, much smaller) type that may have had a hand in the early formation of the universe... and therefore of everything that's happened since.

Or maybe not, but they have been proposed by serious cosmologists as one possible (if unlikely) explanation for the mysterious dark matter that makes galaxy formation possible.

Personally, I find it kind of weird to imagine black holes influencing almost every aspect of universe formation.

Almost like a conspiracy...


Oh, and also:

I learned about black holes when I was very young.
Say hello to my childhood nightmare.
Source: https://bigthink.com/starts-with-a-bang/black-hole-hit-earth/


Happy horrors, people! :pinkiecrazy:

Well, that's my science mythopoeia done for the day. Thought I'd try something different and tackle an astronomy topic, as it's a subject I have a strange attraction towards (geddit!? :rainbowwild:).

If you want something lighter and fluffier: how about them Pillars of Creation, eh? Beautiful stuff.


OK, that's enough for now. Till next time! Impossible Numbers, out.

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Comments ( 8 )

Also also, I am inordinately proud of the fact that I'm the first blogger on Fimfiction to use the phrase "Schwartzchild radius". Break the barriers, people! :rainbowlaugh:

One thing that's worth noting: the formula for Schwarzschild radius is only exact for an isolated mass in empty space. That's why you get an absurd answer if you try to calculate the Schwarzschild radius of the observable universe. No, we are NOT living inside a black hole, and anyone who says we are should NOT be trusted!

5697689

Black holes, black holes, black holes! They're everywhere! Oh my God, how deep does this conspiracy go!?

But seriously, that's a valid lesson on overapplying a theory outside its normal territory. I should also think the fact that we haven't imploded into a Big Crunch singularity should be a pretty good clue that we're not currently in a black hole.

That said, there is an interesting question over what happened around the time of the Big Bang, when the universe theoretically originated as a singularity. I always assumed that was the role inflation theory was designed to fill (since it was proposed to solve the "horizon problem"), though I might be overapplying the theory myself. Normally, I see it in the context of explaining its subsequent accelerated expansion rather than all universal expansion.

Still, there's its possible connection to dark energy, which is supposed to explain - once its true nature is deciphered - why the universe's expansion is accelerating today.

I confess I'm just an amateur, though, and possibly an out-of-date one as well.

I remember there being a scare about micro black holes some years ago, as it was theorized they could be pretty abundant. What people didn't understand, though, is that micro means micro. If they're the same mass as a paperclip, then they're not going to pull you in any stronger than a paperclip would. And if you brushed up against one, it wouldn't take enough mass from you to notice, certainly far less than the amount you already lose every day to dead skin cells and hair. If it was big enough to be dangerous, it would also be big enough to see clearly. But then nobody ever accused your average person of knowing much science.

I am also inordinately proud of having the only story on this site to use the word "terlit," which I also bring up at every opportunity.

5697730

But then nobody ever accused your average person of knowing much science.

Yes, I was mainly remembering all the press scares around the Large Hadron Collider. It's massively disappointing how poorly understood science often is, especially by people more into sensationalism than simple sense.

White dwarfs eventually fizzle out and become brown dwarfs

Whoops! Just realized those would actually be called black dwarfs! Brown dwarfs are something else entirely. Correcting that now...

5698121

To be fair, we have no proof that the world didn't end with the LHC. I mean, this all certainly seems like Hell.

5698437

Nah, it's been Hell for a while, long before then. If anything, the LHC creating a black hole could only be described as a cosmic mercy kill. :pinkiecrazy:

I have a very dark sense of humour today...

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