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Elementary particles don't have a size in the way classical objects do, but their wave function is never perfectly localized - they have a non-zero volume in that sense (for electrons in atoms it would be the volume of their orbitals, for example). The larger the center-of-mass energy the smaller the radius of that volume can be. As you increase the energy of e.g. a collision process you can make the system "smaller" and the Schwarzschild radius grows. The two get to a similar length at the Planck energy (2GJ) which corresponds to the Planck mass (~20 microgram) and the corresponding Schwarzschild radius is the Planck length. It's expected that the smallest black hole is somewhere around that. These are order of magnitude estimates, the precise numbers will depend on a quantum theory of gravity which we don't have yet (at least not in a way that we would be able to calculate this).

If there are microscopic extra dimensions and if gravity extends into them then gravity could be much stronger at very small distances. This would effectively mean the Schwarzschild radius is larger and you need less energy to produce a black hole. The energy might be so low that we can reach it with accelerators, so we look for possible black hole signatures at the LHC. Nothing found so far. It's pretty much an all-or-nothing search: If you have enough energy then you expect to produce tons of them and it's obvious within weeks, so we are pretty sure the LHC energy is not enough to make black holes.

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Is there a particular "science for the lay-person" type of book you'd recommend, that discusses things like this without requiring the reader to know the math?

I loved books like A Brief History of Time, Cosmos, and Black Holes and Time Warps by Kip Thorne, for example, but I'd love to read more about black holes (time and space switch inside the event horizon??), quasi-stars, quark stars, proton structure (what does it mean to have force-carriers inside the proton that would have individual masses greater than that of the proton?), etc..

There seem to be so many books out there on these topics that I have no idea how to tell which ones might be what I'm really looking for.

As has been described in a few reply’s already, to make a black hole you have to “squeeze” an amount of mass to a size so small the density will be enough to create a black hole. This size is given by a radius called the Schwarzchild radius. The equation is R = 2GM / c^2 where G is the gravitational constant and c is the speed of light. M is the mass in question. c^2 is a huge number compared the the numbers it is dividing meaning you need a LOT!!!! Of mass (M) for R to be a meaningful to a human scale measurement. As a slight aside, Saying something like shrinking the sun to a sphere 5km across is a little meaningless to most of us.. we understand 5km but we absolutely cannot comprehend the sheer size of our own sun. Back to tiny black holes.. the other part you need to understand is that physics has shown that there is an fundamental smallest distance that still makes sense… that distance is called the Planck length and is about 10^-35m or a decimal with 35 0s and a 1 on the end. So you can see that if the mass is relatively small it will not be able To make a black hole because it would need To be squeezed in to a size smaller than the Planck length.

If making black holes is a really a potential outcome of the LHC I'm mildly shocked we just let the LHC run without some appropriate protections (if that's even possible)

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This was a concern that was discussed quite a bit in pop-science, tabloid, and conspiracy circles back when the LHC was first starting up. In short, these black holes would not destroy the Earth. Due to their small size they grow much slower than they would decay due to Hawking radiation. Even if Hawking radiation works differently than we think at those scales and they don't decay, they grow so slowly it would take eons for them to eat the Earth.

Cosmic rays with way more energy than the LHC bombard the Earth all the time. So the fact that the Earth still exists would tell us that these micro black holes, if they form, won't destroy a planet in less than billions of years.

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Cool thanks interesting to know

Small black holes evaporate faster than large black holes. If you have a black hole with mass as low as 50 neutron masses, it would basically decay instantly, releasing all its energy in a tiny explosion of light and particles. Even a black hole with a mass of 1 kg would only take 10^-16 seconds to evaporate.

PBS Spacetime plug.

its free on youtube, they're very good at explaining difficult concepts that build on previous episodes. plus, its got good graphics that represent the concepts they're trying to build.

the host is an astrophysicist lecturer, they go as far as they can without having to learn the maths.

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2.17645×10^-8 kg or 1.088225×10^-8 kg

1 Planck mass or 0.5 Planck mass

Those would make black holes with a radius of 1 Planck length or a diameter of said length. The reason nobody knows which is which is because we aren't sure how things are "rounded" at Planck scales

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the way you described it it would seem like dark matter is infact primordial black holes that get stuck at a plank length

At this scale though the black hole would rapidly evaporate due to hawking radiation. So I don't think a black hole of only a few quarks could be considered stable enough to count. It would cease to exist quicker than it could be measured.

I recently read A Brief History of Black Holes by Dr. Becky Smethurst. She also has a great series of YouTubes and really good at explaining things IMO. I highly recommend both. Her book is not overly technical.

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What if thats not the case, and every galaxy with a black hole in its center was a civilization with their own LHC and accidently made a black hole.

I can vouche for PBS as well, super interesting videos and the guys voice is soothing af so it works out when you need a bedtime story before sleep

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I listen to the whole video even when I lose the plot on the mathy ones. It's really pleasant.

Because it won’t matter if they do.

Black Holes aren’t special, they still obey the laws of physics outside their Event Horizon. That means Mass is still King.

If the LHC only fires electrons and protons and smashes them together…all they can get is Black Holes made from that mass at best.

Black Holes are not vacuum cleaners. They don’t suck in anything other than what their gravity allows them to. A 50 Solar Mass Black Hole can’t attract anything a 50 Solar Mass Star can’t. A Black Hole the mass of a few electrons or protons would only have that much gravity which ain’t much. It’d have to get lucky to collide with anything in order to “feed”.

Speaking of, the smaller the black hole the less time it has to live before it evaporates away; they’re not eternal. One the size of a few electrons/protons won’t last long and couple that with the sheer amount of luck needed for it to slam into something else in order to feed…well.

Long story short it’s kinda like worrying about someone making a nuke out of a single Uranium 235 or Plutonium atom. Sounds scary but honestly not really a concern.

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Let's unify the weak force and gravity at very small distances so we can have a "Weak electric gravy" force

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It's a theory in the weakest sense of the word. We really have no idea what happens to black holes when they get that small

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What? That's just not how black holes work. As someone in another comment said "Black Holes are not vacuum cleaners".

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Great thanks for the extensive reply! Always love learning about black holes :)

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yes, but wouldn't they also grow if a particle falls into them before they evaporate?

We would measure the decay products, that's good enough. That's the most common approach anyway. We don't see e.g. Higgs bosons flying through our detector either, we only measure the decay products.

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I always thought of it as a kind of binary problem. Either we make one, and it becomes a problem, then it's our problem, or it's not an issue, then it's fine, or we don't make one, and then that's also fine. So either we have a problem, or we don't. And then either everything ends, or it doesn't.

>Speaking of, the smaller the black hole the less time it has to live before it evaporates away; they’re not eternal

Can you explain how black holes evaporate away? I can't see how any mass would escape the schwarzchild radius.

Hawking Radiation. There’s better explanations but the tldr of it is: particles pop in and out of existence all the time by “borrowing” power to pop in and giving it back when it pops out.
Every now and then, a pair of these pop in near a Black Hole. One of them falls into the Black Hole while the other shoots out taking a little bit of the Black Hole’s rotational energy and mass. And I mean minuscule.

Ordinarily this isn’t enough for a Black Hole to evaporate since it’ll consume WAY more matter than it evaporates. But as it stops consuming content, it’ll start -slowly- loss mass from Hawking Radiation.

This process is thought to happen faster as a Black Hole becomes smaller. It’s why massive Black Holes have an absurd theoretical lifespan like 10^100 years and small micro black holes live maybe like an octillionth of a nanosecond.

Btw I also neglected to mention the LHC likely would never be able to make black holes even if everything went perfect. Smallest theoretical Black Hole is a Planck Length wide (smallest unit) and the LHC slamming what they can into each other would make Black Holes about 10-15 orders of magnitude smaller than that…which isn’t possible.

But if you 'feed' them, will that prolong their lives?
Is there a formula that states how much matter needs to be added in what timeframe to sustain the black hole?

I suppose the smallest black hole will evaporate in 1 Plack second. Faster is not possible, so that is in fact the limit of the smallest black hole if I am right?
so the lifespan of 5,3891 x 10E-44 seconds

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Thanks for the recommendation. I watched a bunch of episodes and it is definitely great.

Many Worlds in One by Alex Valenkin(sp), was a fun cosmology read. Some history thrown in too.

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