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A lot of fantasy stories involve someone using magic or technology to solve a problem, only to find out the spell or thing they used to solve their problem was a little too potent.

Let's say a wizard invents an alchemical like spell that creates gold. It's not created from nothing though, it's just transported from somewhere else. The spell turns out to be a little too potent, and the unfortunate person ends up receiving more than he bargained for: all the gold in the solar system.

Note: Assuming the solar system in the story is similar to ours: This is about $2.0 \cdot 10^{21}$ kg of gold1, or about 2.7% of the mass of our moon.

If the spell summoned the gold as one big cube, it would be about 470 km on each side, comparable to the size of a small country. Assume the cube is initially at rest compared to the wizard's position.

What happens to the world? I'm guessing everyone dies, but just how quickly does that happen?

1: I obtained this figure by using the approximate mass of the sun ($2.0 \cdot 10^{30}$kg) with this resource detailing relative abundances: http://www.periodictable.com/Properties/A/SolarAbundance.html. The contribution from other objects is negligible given the uncertainty we're using.

Details:

I haven't explained in detail enough 'what kind' of thing happens with the stuff that's in the place where something's teleported to. The details can be important with this scale. (e.g. Doctor Who style, or Steins gate style?). You can assume the Doctor Who variant: so you 'swap' the location of the stuff being moved (there's no temporary absolute vacuum). Let's also say that the physics of it prefers a low-energy, high-entropy solution, but we arbitrarily award entropy for putting a particle closer to where the wizard pointed to. So right at the epicenter the stuff is probably embedded into the earth a bit, but mostly towers up into the sky. It's also ordered randomly.

It's also true that the average temperature of the material is something on the order of $5 \cdot 10^6 K$ (as our gold mostly comes out of the center of the sun...). However, if you calculate the amount of thermal energy that equates to about 650 kJ per gram, it's far less than what you'd require for the $\Delta v$ (at least $570\hspace{1mm}\mathrm{kms^{-1}}$, which would take far more energy per gram2), or the kinetic energy because of all the random speeds the particles have. You can assume the magic solves these effects: it uses the thermal and kinetic energy (down to room temperature and being at rest wrt. the wizard) to power a small part of the spell (the other energy comes from unobtanium).

2: Figure obtained by subtracting solar escape velocity at earth's position from that on the sun's surface.

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  • $\begingroup$ Does the wish preserve both linear and angular momentum? $\endgroup$ – Cristobol Polychronopolis Jun 22 '18 at 18:18
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Monica Cellio Jun 26 '18 at 3:25
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tl;dr

I'll study the macroscopic consequences on Earth, since the question could be addressed from a lot of different points of view.

Assumptions:

  • Both momentum and angular momentum of Earth are conserved.
  • The gold starts at rest with respect to the Earth (sorry, no Chicxulub-impactor speed)

Main outcome:

  1. It will probably break/heavily sink Earth's crust, causing—at least—huge massive earthquakes, very likely lava flows and, if the place is close to the sea, floodings.

  2. It will also slightly change the Earth's orbit and spin. And depending on the location of the gold, its tilt, which would drive world-wide climate change.

Updates:

  1. I've added some considerations about the latitude at which the gold appears (thanks to Otto Abnormalverbraucher).

  2. Added two figures for perspective


Details

Your calculations seem right, assuming the $1\times10^{-7}\%$ solar abundance is by mass (which seems to be the convention).

  1. Earth crust's thickness varies from 6 to maybe 70 km. So a cube of 470 km a side will undoubtedly start sinking it and will most likely break it. Gold ($19.3\,\mathrm{g/cm^3}$) is much denser than the crust ($2.5\,\mathrm{g/cm^3}$), the mantle ($4.5\,\mathrm{g/cm^3}$) and even the core ($\sim12\,\mathrm{g/cm^3}$). Ice alone can sink land masses, and its melting may make land masses rise again. The effect, with a lot more mass and all of a sudden (ice is less dense than gold, may be a couple kms thick and has taken decades to melt) will have a much more dramatic effect.

    To put things in perpective, consider the comparison of size between the Earth, its crust, and the cube:

    enter image description here

    • The blue dot is Earth's center.
    • 1 px in the original image is 10 km, the crust is on average like 2 pixels thick. It would break, wouldn't it? Luckily I drew this with paint, so you can see the pixels (no antialias; click to see the original size).
    • If you see a quarter of an ellipse, it's most probably your screen's fault: Earth's polar radius is about 2 pixels less than its equatorial radius. Now let's compare the cube to some popular layers of Earth:

    enter image description here

    • The cube is golden (hahaha, funny, right?)
    • The sea is dark blue, gray is litosphere/crust. I tried to fit the crust's maximum and minimum thickness in the figure
    • The Earth's mantle is in orange
    • You can see the heights of Mt. Everest and Mariana Trench (width not to scale, I have no idea about that, to tell the truth)
    • The two light blue layers are the Troposphere (where life and airplanes happen) and the Stratosphere (it has the ozone layer in the bottom; at the top, pressure is 1/1000th of standard air pressure)
    • The dashed line is where outer space is considered to begin (although you can find a few air molecules even above the cube)
    • The purple band is low earth orbit (LEO). If your world has artificial satellites and the cube is in the equator, some will crash. If the cube didn't sink nor loose shape, all satellites on LEO, including space stations would eventually crash.

    Side comment: this would be an effective method to sink the Netherlands entirely and permanently... or Germany:

    enter image description here

  2. You are adding $\frac{2\times10^{21}}{6\times10^{24}}\approx0.03\%$ to Earth's mass. This affects Earth's spin and the force with which the Sun attracts Earth.

    • The gold will change Earth's moment of inertia. Assuming angular momentum is conserved AND the gold appears at the equator, this will slightly change the angular velocity of Earth's rotation:

      $L=I_0\omega_0=I_1\omega_1\rightarrow \omega_1=\omega_0\frac{I_0}{I_1}$, now, putting the gold as a point mass, and the Earth as a solid sphere for simplicity:

      $I_0=\frac{2}{5}m_\mathrm Er_\mathrm E^2$

      $I_\mathrm{Au}=m_\mathrm{Au}r_\mathrm E^2$(*)

      But $I_1=I_0+I_\mathrm{Au}$, so $\frac{I_0}{I_1}=\frac{I_0}{I_0+I_\mathrm{Au}}=1-\frac{I_\mathrm{Au}}{I_0+I_\mathrm{Au}}$, and we can simplify by $r_\mathrm E^2$

      $\frac{I_0}{I_1}=1-\frac{m_{Au}}{0.4m_E+m_{Au}}\approx1-\frac{10^{21}}{0.4\times6\times10^{24}+10^{21}}\approx0.9996$

      With a slower angular momentum, Earth's rotation will take longer, namely $\frac{86400}{0.9996}-86400=36\,\mathrm s$ longer. Which is slight, but enough to mess time measurement quite a bit.

      (*) If the gold mass does not appear at the equator, we would have $I_\mathrm{Au}=m_\mathrm{Au}r_\mathrm E^2\cos^2(lat)$, the higher the latitude, the smaller the change.

    • Now, rotation is supposed to drive mass to the equator (hence the faster the rotation, the higher the body's flattening, compare Jupiter's 6.5% to the Moon's 0.1%). If the mass suddenly appears far from the equator would mean a mixture of a change in the earth's overall shape (the geoid and land masses) and in the rotational axis, which would affect the axial tilt. Even a slight change in axial tilt would in turn affect seasons and climate: Consider that a change in less than a degree in axial tilt, made the Sahara a desert.

    • Assuming momentum is also conserved, the speed of Earth relative to the sun should also change. Mass is said not to affect a body's orbit, provided speed remains constant. A slower speed would mean a closer approach to the sun after half an orbit (expect more sun radiation the next season).

      $p_E=m_0v_0=m_1v_1\rightarrow v_1=v_0\frac{m_0}{m_1}\approx v_0\frac{1}{1.0003}\approx 0.9997v_0$, but how closer will the closer approach get?

      This can be estimated using Hohman transfer orbit's equation:

      $\Delta v_1 = \sqrt{\frac{GM_\mathrm S}{r_1}} \left( \sqrt{\frac{2 r_2}{r_1+r_2}} - 1 \right)$, where $G$ is the gravitational constant, $M_\mathrm S$ is the mass of the sun, $r_1$ is the Earth's orbital raduis (assuming a circular orbit prior to the appearance of the gold, for simplicity) and $r_2$ is the new close approach.

      Now we want to know $\Delta r=r_2-r_1$ from a known change in speed. Taking into account that $\Delta v$ is proportionally small, we can solve for $\Delta r$ and linearize:

      $\Delta r=\frac{4\times\Delta v\times r^{3/2}}{\sqrt{GM_S}}\approx1.7\times10^8\,\mathrm m$, about a couple hundred thousand kilometers, or a 0.1% closer. This is less than the actual difference between the current perihelion and aphelion, so probably the axial tilt of Earth will continue to drive seasons. Temperature could increase by a (small) fraction of a degree, unlikely to be noticeable in yearly weather's variation.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Monica Cellio Jun 24 '18 at 4:37
  • $\begingroup$ One point you don't seem to have addressed is the strength of gold. It's rather soft an malleable, more so than most crustal rock, so that at the same time the cube is sinking into the crust, it's collapsing under its own weight. I'm guessing that this would shove large amounts of crust sideways, causing really major earthquakes everywhere. $\endgroup$ – jamesqf Jun 25 '18 at 18:27
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What happens to the world depends largely on the nature of the magic used.

If for example, the magic respects conservation of energy, then the gold is going to arrive in a variety of states and temperatures. The portion stolen from the sun's core will be a little warm, maybe even gaseous. With a such variety of temperatures all forced into one cube the result would probably be an explosion.

If the magic also respects conservation of momentum then your gold cube is only going to stay cube shaped for a millisecond. In its pre-summonsed state, each part of that golden horde was rotating around (or within) the sun on a separate vector and at a separate velocity. If all that motion is maintained across the summonsing, the result will probably look a lot like an explosion.

Now let's imagine the extremely rare case where the world builder is actually nice to their characters and allows the magic to solve all the problems inherent in galactic scale grand theft... the poor souls still have to deal with physics. Gold is heavy. Something tells me that if you stack a bunch of gold coins in a 470km tower under earth level gravity, the coin on the bottom is going to be under a lot of pressure. Maybe even nuclear fission level pressure. So once again, an explosion.

TLDR: an explosion.

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    $\begingroup$ I don't know what would happen, but I think it's safe to say I wouldn't want to be anywhere near there when it happens. $\endgroup$ – Neil Jun 22 '18 at 13:21
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    $\begingroup$ I dont think a nuclear explosion is likely as even in our Sun nuclear fusion only happens due to a combination of heat and pressure, but even in our Sun just heat and pressure isnt enough to cause fusion. Only quantum states that accidentally tunnel into another particle causes that (which the pressure, temperature and lot of Sun mass make likely). On the other hand the gold halfway through all the way to the bottom is likely liquified or even vaporized by the heat from the pressure and moves sideways at high speeds... A gold explosion. $\endgroup$ – Demigan Jun 22 '18 at 13:59
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    $\begingroup$ I think I saw somewhere that stars don't ordinarily fuse elements further than to iron. Now, iron has atomic number 26. For gold, it is 79. It's quite a ways to go from 26 to 79, and stars tend to have radii greater than 400-500 km... so if my recollection is anywhere near accurate, there won't be any pressure-induced fusion near the bottom of the cube. That's not to say I'd want to be under it, though! $\endgroup$ – a CVn Jun 22 '18 at 14:18
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    $\begingroup$ @MichaelKjörling You are right. Fusing gold would be endothermal. And anyway. The radius of even Earth is much more than 480km. (even if its made mostly from lighter elements. $\endgroup$ – b.Lorenz Jun 22 '18 at 14:54
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    $\begingroup$ As the gold falls into the Earth, about 2*10^21*9.8*(470,000)/2=4.606*10^27 joules of gravitational potential energy would be released. That's equivalent to 1.1*10^12 megatons. A trillion megaton explosion is not going to resemble some puny H-bomb. Nor would it resemble the gentle pitter patter of the worlds 6.4 billion megaton stockpile being unleashed across the surface of the Earth. There wouldn't be an explosion. There would be the explosion. $\endgroup$ – gmatht Jun 22 '18 at 15:25
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Too Many Catastrophes

Ok so by magical a cube of 470km appears out of nothing. For mercy I will consider it appears cold and at rest (no need of a gold huge meteor), in a flat desert land and avoid nasty things like all the air moved the volum of the cube moved (the shockwaves per si can make any nuke looks like a small bang).

Also let's say the cube keeps a cube by magic, otherwise you can think all that mass as a sort of high viscouseus liquid spreading very fast as a golden tsunami for over even a bigger area, maybe covering a continent and hitting the sea with nasty environmental consequences.

Note also some of the sea salt is made of gold but I'm unsure how it can affect sea wildlife. For sure the sea can become a slight less dense.

Not the last catastrophe can be the mass of the cube ripping trough the planet crust and reaching the mantle this is very speculative but one can expcet volcanos erupting and earthquakes all around and not even start to think about all that gold sinking to the core.

Let's also make the magic protect the planet rotation, you know what can happen if you concentrate mass in a ball? Well put a small lead pin in a baseball ball side and throw it, thats what they call an odd ball.

If there are sattelites over this planet their orbits can be affect by a huge Mascon (sorry ISS).

Economics

Rulling out all the world destruction thing we still will see bad things happening because gold is valuable because it's rare. Unless some major global power throw all his military at protecting the cube, maybe triggering a world war, gold now is a very ordinary thing. You can have balast make of gold to use in fishery, use it to make water pipes and so on as it now can be as cheap as lead (just a bit less unhealthy).

How gold will trigger an economic crisis depends on your world setup. In a medieval setup kingdoms will slowly change all his currency to silver. Powerfull kings will be less powerfull. In a a more renaissense world the new formed banks sinks, the merchants are almost bankrupt and say goodbay to arts patronage. In a modern earth like society we are screwed, badly. Gold is an important commodite.

The bottom line is: The poor fool wished all the gold of the world is now more poor ans screwed than before.

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Here is a slight variation that tries to take into account the working of the spell in a way that deals with the air displacement, the requirements are:

  1. The spell consumes momentum of whatever it teleports (see OP's edit, I accidentally wasted a lot of my time describing what the cube's motion might look like if the spell optimizes the teleportation process).
  2. The spell actually produces a cube of gold for at least an infinitesimal amount of time, in a non-gaseous form
  3. The spell is designed to avoid instantly killing the witch/wizard that casts it. Let's say the witch/wizard was wise enough to take these two precautions:
    1. the radius of effect of the spell excludes a protective shell around the witch/wizard's body just in case gold is involved in any biological process. (side note: is it? I don't suspect it, but one is never too sure).
    2. when it breaks a chemical bond, it teleports as many electrons as needed to keep the gold atom neutral, i.e. 79. The total polarization of every single gold atoms in the solar system might not be perfectly zero. Given the amount of gold, a slight variations might result in a major thunderstorm, but that also gets too impredictible to my taste.

I will assume the spell works like this:

  1. Locate all gold atoms in the radius of effect of the spell. Exclude any gold atom that might be present in the witch/wizard's body.
  2. Sort the atoms by distance from the witch/wizard
  3. Teleport the first atom where the wizard demanded
  4. Teleport the next atom to a position randomly chosen in the vicinity of the cube's forming surface, excluding the face touching the ground. Any atom's momentum is consumed in the process, but the relative electron/nucleus momentum is maintained.
  5. Wait for a small time interval $dt$, then repeat steps 2,4,5 until atom list is exhausted or spell caster is dead.

This will result in the gold atoms in the ground just beneath the spell caster to be teleported first, forming a small ball of gold that first crystallizes to a cubic arrangement, as this is the preferred lattice structure of gold.

All atoms would then gently attach to the surface and conform to the cubic lattice already in place. Therefore each face of the cube would expand by 1 atom per 5 $dt$ on average, leading to a cube of side: $$L(t) = a\times \left(\frac{t}{5~dt}\right)^{1/3}$$

where $a$ is of the order of $10^{-10}$ m. The important point is that because of this power 1/3, the perceived velocity of the face by the witch/wizard gets smaller and smaller.

Let us just assume that $dt$ is chosen (perhaps automatically adjusted over time, letting $dt = f(t)$) such that this expansion pushes the air and everything else around "gently", effectively a quasi-static push, raising the radius of the atmosphere a bit.

Now in the vicinity of the spell caster, there might be plenty of gold available, producing a giant cube of gold similar to what the witch/wizard was expecting. Since gold is generally found in alloys, these would shrink progressively, but it gets more interesting as gradually the spell starts tapping into Gold(III) chloride in the oceans. Leaving unbound Cl atoms everywhere. Now, gold is particularly un-reactive, which is part of why it is so valuable and therefore why the spell was cast in the first place. In contrast, Cl is VERY reactive. Although the Cl atoms are neutral immediately after bound breaking, they will react with any organic substance they will find in the ocean. A significant part of it might simply form Cl2 gas, that should quickly start its rise to the surface.

According to Wikipedia, ClAu3 is present in the ocean in concentration of the order of $10^{−8}$ g/cm$^3$. However that can't possibly be the average concentration as it is waaaay too high if you multiply it with the gigantic volume of the oceans (that would be of the order of gigatons of gold if my calculations are correct). Nevertheless, my guess would be that this represents a huge amount of gas. Here is a translated quote from the French wikipedia entry for Cl2:

[Cl2] has a very unpleasant suffocating smell and is extremely toxic because it combines with mucous and lungs' humidity to form acids that attack tissues

Cl2 is much denser than air but much lighter than water. Therefore it will erect from the ocean and creep at Earth surface, intoxicating everyone that leaves close enough from sea level.

It's difficult to say wether this would kill all humans because I don't have access to the total amount of Cl released in this way. If it is small enough it might form a thin layer at sea level? But how thin exactly I could not tell.

Cl2 should be consumed fast though, since it can react with pretty much anything present on Earth's surface. So again it all boils down to how much amount comes out...

It's also quite likely that a large fraction of Cl will react with organic compounds in the ocean way before it reaches the surface, leading to pollutions of some other form. In any case, polluting the whole fricking ocean in just one day would certainly have nasty effects on sea life and climate, with inevitable consequences for us.

All the while, gold escapes all electronic devices of the Earth (we neglect dentistry devices). Now this is not as violent as you might expect, because it goes out atom by atom, reducing very gently its conductivity to zero, bringing the devices to open-circuit conditions. Therefore I do not expect much electrical hazard. The main problems would come from the engine in which they are embedded. As all computers in the world gradually shut down, the commands of engines, planes, trains, boats, stop responding. Planes would certainly crash, as their controls, sensors and communication to the outside all shut down.

I don't know how much electronics are involved in trains but they do have an emergency brake that is purely mechanical (at least in France), so driver might be able to save lives. Automatic track orientation might fail too. Satellites in the area start failing too. Solar cells all stop producing any of the current that no device is consuming anymore anyway.

More importantly, a number of hospital devices cease to function. In general, numerous hazards could be expected from the lack of control over virtually any machine that has an electronic interface. Those in motion come to rest in whatever way. Perhaps gently in a number of cases.

At this stage, the news have been broadcasting on every channel about strange reports of failing engines, car crashes, and fail to report unusual Cl2 levels over the ocean, as this would seem irrelevant in comparison to the much more visual effects of electronics. One by one though, all radios and TVs stop to deliver those news. Fewer and fewer people manage to reach their loved ones by phone or facebook.

At this point, a number of people would perhaps panic slightly.

Those who take their cars to flee find themselves stuck in massive traffic jams that are not regulated by any traffic light. It gets worse as more and more of these cars stop functionning properly in the middle of the road. Added to the overall nervosity, I guess the risks of car crashes is huge.

People in the countryside would probably be slightly less affected but are out of power too, meaning all the refrigerated food is doomed. Those who will survive till the end of this spell could experience some difficulty to feed themselves.

Assuming the cube has reached the point where it has accumulated all the gold from Earth, it starts tapping in the sun, and the witch/wizard starts to back down as it gets clearer and clearer that the cube's advancing front is going to crush anything on its way. Again, there is freedom in $dt$ so running might be unecessary, but the cube is going to be 470 km long ultimately. Out of any transportation mean (the locals have used any animal they could possibly find to carry them as far as possible), the witch/wizard eventually gets exhausted and falls.

The cube rolls over them, breaking loop (5).

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Even ignoring all the other catastrophic effects (magic fixes them all, say), you now have a really, really huge "mountain range". Depending on how much it sinks/spreads out, it still has a really good chance of sticking right out into space (ozone layer: ~50km, "edge of space": ~100km).

Compare to, say, the Rocky Mountains--this wouldn't be as long, but the extra height means that really no weather can get across it. So say you plonk it right in the middle of an air current coming off of the coast. The wet side is going to get a lot wetter, and probably experience a ton of erosion around the edges. The dry side is going to turn into a desert, if we look at the Dust Bowl period that could happen in maybe a decade (or less) and probably also experience erosion as the plants die off (root die off will stop holding the soil). Winds along all sides that run parallel to the sides will probably get a lot stronger.

On top of that, gold seems to be slightly lighter in color (and more reflective, even in a raw state) than most natural surfaces, so that might cause the surrounding area to get a bit cooler (sort of like a reverse heat island). Having a large area sticking out of the atmosphere and reflecting heat/energy before it even gets trapped by the greenhouse effect would probably also cause a strong cooling effect.

(I'm trying to base a lot of this on water currents around large islands and air currents around normal mountain ranges.)

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    $\begingroup$ This is not my area of expertise but gold makes a really good mirror so you may have other issues depending on time of day, angles, and atmospheric distortion. $\endgroup$ – Marie Jun 22 '18 at 19:04
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    $\begingroup$ @Marie Good point--although if you put it on the coast, you no longer need to build navigational beacons for a good ways........ $\endgroup$ – user3067860 Jun 22 '18 at 19:54
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The other answers result in a wonderful "everyone dies" scenario, so I'd rather look at a different interpretation of "all the gold". This is related to the question, but changes one of the assumptions.

In this spell, "gold" applies only to the element where it has aggregated into particles which exhibit the large-scale properties of metallic gold. Individual atoms, gold nanoparticles, and gold suspensions are not transported. Only aggregates large enough to be recognized as gold, such as gold dust in a pan, or nuggets found in rock. And, since gold aggregates are produced by biological processes found only on earth, the spell only summonses gold from the earth. In particular, the gold content of the sun is not included, nor is any undifferentiated gold found in non-biologically active planets summoned.

The resulting gold mound is much smaller. Magic bypasses any negative effects of temperature, momentum, or energy balance. The abundance of gold in the earth's crust is, by two estimates, 0.0011 or 0.0031 ppm. Assume the average of elemental gold 0.0021 ppm, or 2.1 parts-per-billion. I estimate that 1% is in aggregated particles, giving an amount of Magically accessible gold of 0.021 ppb. The mass of Earth is 6x10^24 kg. The total amount of gold summoned would be 1.26x10^14 kg. At 19,300 kg/m^3, the spell yields 6.53x10^9 m^3. This is a 1.86 km cube. Surely this is a lot, but it stays well within the atmosphere, doesn't disrupt global weather, and, although it may cause some local crust compression, doesn't kick off global volcanism.

What it does is make gold worthless, and where it was used for it's chemical properties, things break down. No one has gold to exchange for currency or barter. No gold jewelry. No gold leaf protecting roofs. Electronic connectors corrode more quickly. Some uses of gold may still possible, such as magenta inks and dyes, because they aren't made of aggregated particles, but manufacturing them has to start over since all the metallic stocks have being taken.

So, everybody lives, but life is less sparkly, things break down faster, and, as happened in the Rocky and Bullwinkle Fractured Fairy Tales cartoon, we all start bartering with turnips.

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  • $\begingroup$ "since gold aggregates are produced by biological processes found only on earth" Interesting, but strange. I could not find anything about this. Do you have a source? $\endgroup$ – Renan Jun 25 '18 at 17:00
  • $\begingroup$ I should find one. I remember speculation that most concentrated deposits were from bio-segregation of metals, but i'll need to look around for a proof text. $\endgroup$ – cmm Jun 25 '18 at 22:01
  • $\begingroup$ This wikipedia article en.m.wikipedia.org/wiki/Ore_genesis , contains several examples of how biological processes cause like formations, starting with the Banded Iron Deposits caused when the atmosphere was becominy oxygenated. Regarding gold, gold nuggets result from the action of a particular bacteria, and other biologic processes, such as limestone and metamorphic rock, also are involved. I admit it may be less direct than I remembered, but biology is important to gold ore formation. $\endgroup$ – cmm Jun 27 '18 at 2:18

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