How much gold (Au) is there in the universe? What would be a good way to estimate this?
A very good place to start is here. This graph shows the abundance of all of the elements in the universe by mass… note that the vertical axis is in orders of magnitude. As you can see, gold (like most heavy elements) is not that common in the 'verse: only about 0.6 grams for every billion grams of stuff. I am assuming (possibly incorrectly) that these figures do take dark matter into account.
The data also says that, across the universe, you’ll only find one gold atom out of 250 billion atoms. Not a good way to make a quick buck.
Given the amount of mass in the universe, though, that still does amount to a lot of gold dust strewn across the stars. So how much stuff is in the universe? We don’t really know. But the estimated mass of the observable universe is 3 x 10^55 grams.
Given that all of these figures are correct (a big if), we find that:
(3 x 10^55 g matter) x (0.6 g AU/10^9 g matter)
(1.8 x 10^55 g matter x g Au)/(10^9 g matter)
1.8 x 10^46 g Au in the observable universe.
With the earth weighing in at 6.0 x 10^27 g, that means there’s enough gold out there to make 3 x 10^18 planets the mass of the world out of pure gold. I don’t know how to convert troy ounces to grams, but with gold going at around $400 today, you can count on just one of those shiny worlds being worth a bundle.
The first question is what you mean by “the Universe”. Current thinking is that the Universe is infinite, so assuming that the distribution of gold in the Universe is approximately uniform, there would be an infinite amount of gold in the universe, too.
So let’s say we’re talking about the observable Universe, which is a sphere about 100 billion lightyears in radius centered on us. This gives us a volume of 3.55 × 10[sup]81[/sup] m[sup]3[/sup]. The Universe seems to be flat, so that’s all at the critical density of about 10[sup]-26[/sup] kg/m[sup]3[/sup]. That means that the total mass of the observable Universe is 3.45 × 10[sup]55[/sup] kg. Of that, only about 5% is baryonic matter, meaning matter made of atoms, leaving us with 1.73 × 10[sup]54[/sup] kg of atoms, most of them hydrogen. There are 6.02 × 10[sup]26[/sup] hydrogen atoms in a kg, so that means that there are approximately 1.04 × 10[sup]81[/sup] atoms in the observable Universe. From this graph, about one atom in 10[sup]11[/sup] in the Universe is gold, so that would leave us with about 10[sup]70[/sup] gold atoms. And each gold atom weighs 3.27 × 10[sup]-25[/sup] kg, so that’s a total of 3.4 × 10[sup]45[/sup] kilograms of gold in the observed Universe. To take this further, gold has a density of 19.3 times that of water, so that would be a cube of solid gold 5.6 × 10[sup]13[/sup] meters on a side, or 56 billion kilometers.
Using Chronos’ figure, our cube of gold weighs 32.15 x 3.4 × 10[sup]45[/sup] = 1.093 x 10[sup]47[/sup] Troy ounces, which at the current market value of US$401.40 per Troy ounce would be worth US$4.388 x 10[sup]49[/sup].
Actually, The predominant belief is (and has been for decades) that the universe is finite.
However, many theories say it is boundless (i.e. it doesn’t have an “edge” or “end”. Perhaps that’s what you were thinking of. This has to do with the shape -or even the definition- of space-time. The surface of a sphere for example is finite but has no boundaries. In the first half of the 20th century it was commonly believed that space-time was an external absolute framework independent of the Big Bang (though there were significant theoretical suggestions that it might not be, as early as the 1920s, based on relativity, etc.). Current thinking is that space-time as we know it, right down to the physical laws we observe, “crystalized out” of the Big Bang. The progressive unified theories of physics show how each of our known physical forces is just a manifestation of a single Grand Unified Force originatig in the big bang. Without the energy and mass from the big bang, spate-time is meaningless, and certainly wouldn’t be what we mean by the ter,
The observable universe is a different issue. You could place its limits at the distance where the Hubble expansion reaches the speed of light (or redshift is infinite). The exact figure is trickier to calculate than many figures given in books, because the farther away you look, the further back in time you are seeing, and faster those regions of the universe are seen to be expanding (Mutual gravitational attraction has steadly slowed the rate of expansion over time)
More importantly, it’s been quite a long time (1950s? 1960s? Earlier?) since any serious theory suggested that the mass of the universe might be infinite. All current research relies on the presumption that the mass of the universe is finite. If it were infinite, for example, there would be no question that the universe was gravitationally closed (will eventually collapse into a Big Crush) In fact, right now, we’re having difficulty finding enough matter to explain the structure of the galaxies or the observed “flatness” of space-time. Hence the Dark Matter theories.
(If space is positively curved, it means there is not enough mass to halt the expansion and bring about a Big Crush, so it will expand forever. If it is negatively curved, then the universe has enough mass to bring it full circle. At present, experimental evidence suggests that it is extremely flat on average, within the limits of our ability to measure. “flat” is be boundary between the two curvatures, and indicates a finite mass – i.e. not enough mass to be cause negative curvature.
I may have reversed positive and negative above [I sometimes do] but I’m pretty sure I got it straight this time)
To inject a factoid in this discussion, I heard a Jeopardy question a few weeks ago that asserted that all the gold ever mined from the Earth would make a cube 50 feet by 50 feet by 50 feet.
Hijack territory but what the heck…
I have heard similar factoids over the years. With all of the government bullion, collectors of coins, jewelry and industrial use of gold I have a hard time believing that there was only that much mined. Can anyone verify this?
What exactly is a ‘factoid’, anyway?
One hundred twenty five . . . thousand . . . cubic feet seems . . . okay, maybe it’s not too much. I hadn’t done the math before I clicked the reply button.
Yay, it’s my 300th post, and it’s taken me not much more than a year to accomplish!
Another dubious factoid along the line of the 50X50X50 cube that I read was that if we mined the ocean floor, we could get enough gold to give every person on Earth 6 pounds of the stuff.
I believe that came from Time Magazine, to take it for what it’s worth.
Great answers to a random question that came up at work today!
Chronos’s 56 billion kilometer per side cube of gold makes me wonder whether such an object would collapse under its own weight!
The figure I’ve always seen quoted is 60’ x 60’ x 60’. I’ve spent some time studying gold. I’ve seen this in every piece of information I’ve gotten (broker’s reports, mining reports, I think even a US Treasury report too), but annoyingly can’t find them.
QED, I think that the value of all the gold in the universe, should it be extractable, would be significantly less…
Factoid - term commonly used to indicate a piece of trivia, originally means a fact erroneously reported by a newspaper.
As Chairman says, apparently the figure is supposed to be 62 feet on each side, weighing 4.2 billion ounces. The source here is Northwest Mining Association, reporting a figure given to them by the Gold Institute. I couldn’t find any such trivia on the Gold Institute website.
Considering that much money doesn’t actually exist, yes. But I did say at current market rates.
If the universe is only a dozen or so billion years old, how could anything 100 billion light years away be observable? The light/radiation/whatever would have needed to begin travelling toward us 80+ billion years before the big bang? I’m confused…
Actually, Chronos was being conservative. A figure of over 150 billion light years is now being touted. Here is a nice, readable explanation.
Actually, Chronos was being forgetful. I couldn’t remember the exact number, so I just went with the order of magnitude. Which makes all of my multiple-decimal-place calculations after that point somewhat extraneous, I admit.
And KP,
The predominant belief has been for decades “we don’t know, but it might be finite.”. The current predominant belief, however, is that the Universe is exactly flat, or very near to it, and there is no evidence that it has any nontrivial topology. Flat with trivial topology (along with the usual assumption of homogeneity) implies that it is also infinite. If the Universe is infinite in volume, then by the assumption of homogeneity, it must also be infinite in mass, which is perfectly consistent with most current cosmological models, so long as the density is finite.
ataraxy22 is quite correct that a solid chunk of gold that large would, in fact, collapse under its own weight. One need not even know any of the structural properties of gold to determine this, since that mass would have a Schwartzschild radius of about 5*10[sup]18[/sup] meters, well larger than the size of the cube itself, so it would collapse into a black hole.
That would be a big waste of gold.
OK, so your gold sphere would collapse into a black hole.
But what’s the biggest gold sphere one could have that wouldn’t collapse into a black hole? Actually, since we want the gold to stay gold, we’d have to make it small enough that it wouldn’t collapse into a neutron star either.
I have no idea how one would go about calculating this, but what would be the largest sphere of gold you could have, and still have 99.99% of it stay gold for a billion years or so? It has to be small enough that it doesn’t heat up to stellar temperatures so no appreciable fusion/fission is going on. Let’s assume our gold mass is in intergalactic space so it won’t be picking up any appreciable space dust or comets, ignore all that. We wouldn’t want any hideous water oceans on our lovely gold planet, would we?
Once we’ve calculated the largest mass that would allow stable gold, we could calculate the size and surface gravity of the thing.
“Stellar temperatures” cause fusion in hydrogen (and eventually, helium, lithium and so on, up to iron, where things get mighty interesting for a few seconds). I’m trying to imagine what kind of energy you’d need to cause gold to fuse, but I’m pretty sure that you’d have a neutron star (or BH) long before any gold fusion action was goin’ on.
I agree that you’d probably be right at the edge of neutron starhood before you’d get fusion, but would high temperatures cause gold to fission? I’m not really up on my nuclear physics, but my understanding is that all elements heavier than iron aren’t at energetic equilibrium. But I’m not sure if increasing temperatures would be more likely to cause transferric elements to fission.