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In this overly litigous society, one can't be too careful.
Though
the odds may be low, think of the liability issues which
could
ensue should an unsupervised child, a family pet, or simply
an
angry or intoxicated adult human
user crush your product to
fit within a sphere of radius smaller
than the product's
Schwartzchild radius -- the radius below which the mass in
question will become a black hole. Even though the
evidence might be hard to retrieve in a resulting legal
dispute, we're talking -major-
liability here, people. Yikes.
While producers of most service 'products' (consulting firms
and
the
like) may breathe fairly easy, those in recycling or the
manufacturing
sector might heed this risk and start voluntarily printing
Schwartzchild warning labels on their products. Simple,
clear
text would suffice, such as 'Warning: Do not crush to smaller
than this
circle:', followed by a circle of radius Schwartzchild for the
product at its most massive (spongemakers take note:
calculate for frozen mercury-logged sponge).
The circle in question would be quite tiny (and might get
distorted to even smaller size should the product be
crushed
at all), but this warning should suffice to absolve your
company of liability in the case of consumer black hole
mishaps. Let's hope so.
Product Warning Labels
http://dorsey.frees...quotes/physics.html
One of my favorites :) [phundug, Oct 04 2004, last modified Oct 05 2004]
Black hole evaporation
http://www.alcyone....le-evaporation.html
Lots of equations [kropotkin, Oct 04 2004, last modified Oct 05 2004]
Lifetime of a black hole
http://library.thin...h/advance/core8.htm
[kropotkin, Oct 04 2004, last modified Oct 05 2004]
The black hole of negrav
http://authors.wiza...lack-hole-of-negrav
The Unorthodox Engineers [8th of 7, Dec 17 2010]
[link]
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So it's not the minimum radius needed to keep my nephew from swallowing the thing, then... |
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Perhaps that's the Steelechild radius? |
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I guess it would have to take into account the increased gravitational pull as the object is squished further, so the circle is probably bigger than you would first imagine, maybe even a few micrometres in size. |
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You'll need a Schwartzchild hotline for the inevitable emergency...though I doubt a black hole less than a few dozen atoms across would be much danger. |
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"Watch for faint, sparkly lights floating in air. It's also useful to listen for the sound of rushing air, like a leaky tire." |
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<Schwartzchild hotline> ;-b |
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Operator [picking up phone at random intervals]:
Hello?
Hello? |
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//though I doubt a black hole less than a few dozen atoms across would be much danger.// |
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Are you kidding??? Think about it for a second. Even a tiny black hole, with its gigundous gravitational pull, would accelerate towards the center of our planet. Considering its incredible weight, it would fall straight through the ground. Anything it touched - or which came within the event horizon - on the way down would instantly be sucked into the black hole, increasing its mass. Our entire planet would eventually get sucked in to a pinpoint no larger than...well, the point of a pin. |
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Care to prevent that? Make Schwartzchild radius labelling manditory. |
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Yes, but a small black hole wouldn't mass much or cause much damage while it was falling. I doubt it would gain enough momentum while falling to the center of the earth to resurface. Eventually it would settle to the center of the earth, suck up a little molten iron and not bother anyone for a long time. Might cause a few earthquakes on the way down... |
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"Operator [picking up phone at random intervals]: Hello? Hello?"
That's the Schrodinger hotline. They periodically check on you to make sure you're still alive. Or not. |
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Suck up a little molten iron and not bother anyone? Since the iron is liquid, it would all get sucked up, because as iron was removed, the remaining iron would gravitate towards the center and fill its place. Once its all gone, we've got the problem of a vaccuum in the center of the earth (think reverse volcanoes). Magma would flow the opposite way, eventually creating tunnels from the core of the earth to the surface. All of our air would get sucked into the center of the earth and disappear from our universe forever. |
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This is, of course, assuming that the earth could withstand the stress of having a hollow center, and not collapse in upon itself before this could happen. |
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«The circle in question would be quite tiny (and might get distorted to even smaller size should the product be crushed at all)» |
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What about meta-Schwarzschild-warning labels? "If this warning were to be shrunk to a radius of less than 10^-30 m it would itself form a black hole." |
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Hmm, methinks we need some more SI prefixes to talk about these conveniently... |
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...which we could use to support the orbital tower we need to mine the sun... |
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Viel dank, Jutta -- I worried post-post that I had it wrong,
given Rothschild ('red shield'). Can anyone think of
another English dictionary word that has 11 consonants
and 2 vowels?!... |
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(+) I’m imagining a line of Schwarzschild products, starting with their notoriously troublesome waste disposal…
“Schwarzschild’s! How may I direct your call?”
“Oh hi, I just bought one of your black hole 9000 waste eliminators…”
“And you're having trouble getting your trash items to go down the hole, right?”
“Why yes! It’s so tiny…”
“Ain’t it something? But honey, you need to spaghettify your trash before you singularize it.”
“Singularize?”
“Didn’t you read the manual?”
“Manual?”
“It came with the unit…the book by Steven Hawkins?”
“Oh gosh, that’s what I’ve been trying to get down the hole…”
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The one thing that no one takes into account when thinking about miniature blackholes is how much mass they actually contain. In the context of this idea, I could turn a penny into a black hole. Sure, *extremely* close to it there might be an issue with gravity. This issue is diminished with the inverse square as your seperation increases. In fact, if you had your thumb one penny radius away from the black hole, you'd experience the same graviational pull as said penny at that distance. |
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Throw in the fact that these things are infitesimally small, and you realize that pretty much the only way they can accumulate mass is by colliding with an atom. How often does that happen? Think about a neutrino and the size of the tanks we use to see one or two collisions a year, even though the neutrinos are constantly flying through. They're pretty rare, to say the least. |
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However, if the black hole were signifigantly larger, and had the mass of a large mountain in it, then we might all have a reason to worry. |
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I like the idea, but after some calculation I'm not absolutely convinced it is necessary. This is because of the extremely short lifespan of small black holes, which decay by emitting Hawking radiation. Based on the above links, the lifespan of a black hole is: |
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where t is the lifespan in seconds and m is the mass in kilograms. |
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So a black hole weighing a kilogram would last about a tenth of a femtosecond, one metric ton (1000 kg) would last about 100 nanoseconds, and one weighing 1000 tons just over a minute. Placing these warnings on drinks cans would be pretty pointless unless your reactions are really fast. |
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// Since the iron is liquid // |
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Correct me if I'm wrong, but they seem to think it's soild. I'll find a link when it's not so hot. |
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yes, the centre of the earth is solid iron
And a black hole made from the average consumer product would be amazingly tiny (one kg makes about 1*10^-27 m radius) it would have to actually touch the nucleus of an atom to do anything |
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likely the black hole (unaffected by friction, air resistance, etc) would orbit around the centre of the earth (it would be a strange orbit though, because gravity drops as you go towards the centre) |
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Also, there is reason to believe that there is a minimum size that can become a black hole, a mass of 10^-5g will be so dense that the size of one proton would contain all the mass of the entire universe |
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See also: "Artifact" by G. Benford for lighthearted discussion of astrochew-chews in eccentric subterranean orbits, and, of course, E.R. Burroughs's "Pellucidar" series of scientific papers for reports on hollowed-out interior o' Earth, et al. (Or is it et it all? Damn planetary core gets all molten and slippery the minute you add neutronium...) Seriously, though, if you had a big, useless chunk of mostly rocky planet and a little black hole, *could* you use it to create a large hollow interior? I imagine it would eventually become more fragile than a tea cup, to say nothing of weirdness regarding interior surface gravity... |
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// big, useless chunk of mostly rocky planet and a little black hole, *could* you use it to create a large hollow interior? // |
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David Brin's "Earth" for the doomsday scenario, but as has been said above, the mass of a consumer product black hole would be no greater than the consumer product. As a result,
it actually pulling in an atom would depend on it actually hitting the atom, at best a rare occurence. |
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So the black hole would decay within femtoseconds, and would be unlikely to grow in this time. I don't see how this diminishes the legal or moral need for the warning lables though. |
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Seeing as how the Hawking radiation decay is essentially a perfect mass-to-energy conversion, I think the real issue would be the rapidly expanding fireball and resulting mushroom cloud. A 1kg black hole would, (as [kropotkin] stated) evaporate in 1/10 femtosecond, and release the equivalent of a 20 megatonne nuclear explosion. Which is around 1000 times larger than Hiroshima. In fact, a nuclear bomb takes many many times longer to explode than 1/10 femtosecond, although for all intents and purposes that doesn't really matter. |
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So I'm saying the warning label needs to be a long way away to be useful. Beyond the blast radius, at least. |
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[custard], the warning label is designed to be read -before- the explosion, not after. |
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Ah, so maybe a "WARNING: you must be X far away to ensure safety, should this item be compressed smaller than this circle . " |
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"WARNING: Do not fill this gravity well above the Chandrasekhar limit.
Packed by weight, not by volume; contents may settle during
gravitational collapse." |
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