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I'm considering a scenario where Humans cannot live on Earth anymore, and need to settle other planets. Some physicist I follow on YouTube like to remind us that almost no mater what we do to Earth, it will always be easier to fix it, then to terraform other planets. So I'm considering extreme scenarios...

Apart from being outright destroyed, being "grey-good" is probably the next worst thing that can happen. But I would imagine that "grey-goo" would have been designed with some purpose beyond just multiplying itself, in particular, producing something "valuable". So I imagine they might turn the Earth into gold, titanium, uranium... assuming grey-goo can somehow transmute materials. But a funnier alternative is the paperclip maximizer.

So my question is, what would happen if the Earth was turned into (steel) paperclips? Would they be "denser"? Would the Earth shrink? Would it cause the paperclips to melt into on giant ball of molten metal? Would the magnetic field become much stronger? Would it somehow disintegrate, causing the rest of the solar system to be "infected" with grey-goo?

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    $\begingroup$ A classic "gray goo" scenario requires that the assemblers produce more assemblers; that's how a tiny contamination becomes an existential threat. If they're making paperclips instead of assemblers, there's no chain reaction. $\endgroup$ – Cadence Dec 10 '19 at 19:46
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    $\begingroup$ @Cadence Sometimes the paperclip optimizer problem is phrased in a way that leads to a surplus of assemblers followed by a sudden transformation of the raw materials remaining, and the raw materials in the assemblers, into paperclips. Just depends on who you talk to and how they treat paperclip optimizers. $\endgroup$ – Cort Ammon Dec 10 '19 at 19:51
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    $\begingroup$ Just to be clear: the question is "if we took the 'paperclip maximizer' analogy seriously, and actually turned the bulk of Earth into paperclips, what would be the physical side effects?" $\endgroup$ – Cort Ammon Dec 10 '19 at 19:52
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    $\begingroup$ @CortAmmon-ReinstateMonica Yes, that is what I mean. Obviously, some of the mass is made up of the nanobots themselves. But only a small fraction, since the goal is to make as much paperclips as possible. I could imagine the last nanobots turning each other into paperclips when all the rest was transformed, but I don't think it will affect much the property of the planet as a whole. $\endgroup$ – Sebastien Diot Dec 10 '19 at 20:30
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    $\begingroup$ I knew that Microsoft Paperclip thing from the early 2000’s was trouble! $\endgroup$ – Darius Arcturus Dec 10 '19 at 21:39
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To turn Earth completely into paperclips, you basically have to gravitationally unbind it otherwise you just end up with an iron-cored planet again when gravity and smushes everything together and there's no realistic way that anything in the middle could clip paper. What self-respecting paperclip maximiser would tolerate that?

To fully unbind the Earth would take 2.9x1031 joules... a largely impractical amount of energy to generate, roughly equivalent to the entire output of the Sun for a whole day (which you'd need a whole Dyson shell to harvest anyway, which you don't have). It'd take 2 billion days of power from a whole-Earth surface of perfect solar panels to get that much oomph. You'd basically have to build your infrastructure in space first, possibly by dismantling the Moon for materials, then start work on the Earth. And you'd need a lot of patience, but lets assume the maximiser has that.

But! Is this all really necessary though? Paperclips, after all, are reasonably well defined... you can't just make any old rubbish! They should be made of steel, and steels have recipes.

An acceptable carbon steel would be 2.1% carbon, and almost all of the rest would be iron. Earth is 32.1% iron, but only 0.05% carbon. That's enough for a handy 1.27x1023kg of paperclips, but (co-incidentally) the maximiser would only have used up about 2.1% of Earth's total mass. Almost all the iron would be untouched, for lack of carbon. Dismantling the moon won't help either... the moon has an even smaller carbon reserve than Earth. The Earth's crust weighs about 2.7x1022kg, so the maximiser would have done little more than scrape the surface. All of the water, oxygen, silicon and all the rest along with almost all of the iron would remain, on a sterile dead world, covered in paperclips and with a faint halo of distantly orbiting paperclips. Here and there you'd find assembler robots waiting patiently for the next carbonaceous asteroid to make landfall...

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  • $\begingroup$ So, in short, we only have a paperclip "crust", but since the nanobots would be starving for carbon, no human would dare set foot on it again. I guess that works for my purpose. $\endgroup$ – Sebastien Diot Dec 11 '19 at 10:04
  • $\begingroup$ Just looking at the masses, the layer of paper clips on the earth surface would be something like a few kilometers thick? That should be totally sufficient for OPs purposes. $\endgroup$ – quarague Dec 11 '19 at 15:52
  • $\begingroup$ The OP did specify elemental transmutation, so carbon limits wouldn't stop the assemblers. $\endgroup$ – jdunlop Dec 11 '19 at 18:38
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Disclaimer: Speculative

Assuming all available matter on earth were transmuted into mid-steel, earth would be slightly denser - Earth's average density is 5.5 g/cm^3, while mid-steel is 7.7 g/cm^3, but that does seem like a very unambitious paperclip maximizer. Among other things, past a certain mass of paperclips, the "core" of the paperclip planet would indeed melt, particularly if that pesky moon is still inducing tidal stresses. So flinging paperclips into the void makes sense, both from the perspective of keeping them as paperclips, and also as a means of seeking out more matter to convert to paperclips. (Like the pesky moon, for starters.)

The larger problem (and one common to a lot of grey goo problems) is power. Elemental transmutation, paperclip production, replication - all of this is pretty energy-intensive, and unless they can directly convert matter to energy (which isn't generally a nanoscale operation), you're going to have a lot of precursor steps to "Earth is all paperclips".

In general, however, if we assume earth's transmutation to Paperclip!Earth is a fait accompli - if you gather enough of anything in one place, you get something that acts a lot like a planet. It'd be slightly denser, the magnetic field would be largely unchanged (it's a solid iron core that gives us our magnetic field, so steel is close enough), and the only thing that would cause disintegration is a paperclip maximizer working for the Paperclip Diaspora.

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  • $\begingroup$ If I remember well, iron is like the "lowest atomic energy" element anyway (or something like that), which is why eventually the oldest stars to survive in the universe will turn into iron. So it would imply that, in theory, turning everything into steel, or at least iron, would produce a surplus of energy(?) $\endgroup$ – Sebastien Diot Dec 10 '19 at 20:34
  • $\begingroup$ OTOH, if I'm wrong, and a lot of energy has to be added, then that will, unfortunately, also significantly affect the planet. Clearly, we know that elements can be transmuted into each other, but we don't know if, and how, this could be done at a nano-scale, if at all. But this part is not critical to the question itself. $\endgroup$ – Sebastien Diot Dec 10 '19 at 20:37

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