This was famously answered by Archimedes in his Eureka moment: https://www.longlongtimeago.com/once-upon-a-time/great-disco...

No, that measures volume, not gold content. Anything at least as dense as gold, maybe with with gaps in it to match the density, and a layer of gold around it is indistinguishable from pure gold this way.

A more reliable and still relatively cheap test is via conductivity.

Yes IIRC cutting with Tungsten is quite good at circumventing these tests

That's a children's parable. You can easily defeat the test by using two metals, one denser than gold and one lighter, whose combination matches the density of gold, and then putting a veneer of gold on top of it.

You can nowadays look at a 3D-plot of internal density in an X-Ray computed tomography. On the chance that somebody mixed up an alloy that has the exact same density and X-Ray density as gold, you can try X-Ray absorption spectra which depend on nuclear resonances of different nuclei, so would conclusively prove presence and amount of non-Gold material.

And you can do activation analysis, where you activate the ingot with neutron radiation such that Gold isotopes form and decay. You then measure the decay gamma radiation spectrum and look for decay lines that are not gold but another material. This is non-destructive, but will make that ingot slightly radioactive for a while, but nothing that a few weeks of patience to wait for the decay can't fix.

You know slightly different NMR machines are used to scan entire humans, right? They only really differ in scan pattern for this aspect. That's IIUC just a software change.

Afaik not really. The ones that scan humans are tuned for a specific proton resonance frequency, so they basically measure hydrogen density. But you get a 3D-Plot because they do a computed tomography of that density.

The chemistry NMRs are spectrographs, so you dial through a whole frequency spectrum and look at the reflected/transmitted signal. With that you get different peaks for different nuclei plus some deviations for crystal or molecular structure.

But I have to admit, that I'm a little rusty on that topic, so you might be right anyways.

Yeah right I looked again and also: MRI doesn't really work for highly conductive (bulk) samples: you can't get the RF in/out of the conductor due to skin effect.

Also proton frequency only....

This all sounds kind of expensive to do for every bar?

Usually you draw a representative random sample for these kinds of things. You only test every bar if you detect a problem in the random sample.

It stands to reason that people were not doing this though before Archimedes hit on density.

That wouldn’t work in Archimedes’ time because gold was the densest metal available then.

It could be done now but most of the candidate elements cost more than gold. Uranium looks feasible if the gold veneer will block the radiation which otherwise might tip off the recipient.

Tungsten has almost the same density as gold and costs way less.

19.283 g/cm3 vs 19.254 g/cm3

https://www.metal.com/en/markets/24

Only tungsten is cheaper and heavier than gold and it's tricky to work with

Been to a pawn shop in Hong Kong that deals with gold. They still buy small gold nuggets and simply check by juggling. So probably weight, volume and malleability, and that probably fake golds aren’t a big deal for them.

On the individual scale, something like a Sigma Metalytics resistivity analyser (passes an electric field through the sample, checks to see if resistivity, conductivity, weight or size all match up to what you'd expect from a homogeneous gold sample of that size or weight. On the commercial scale, an XRF spectrometer. Both methods are completely non-destructive, and highly accurate (the XRF more so).

(the two scales are due to price and bulk: the Sigma is about the size of a hardback book and a few hundred pounds, an XRF is the size of a large 3d-printer and many thousands).

Does XRF penetrate the sample? Isn't it a surface measurement?

XRF will go a millimetre or so into the sample AFAIK - it's mainly useful for finding alloy contamination, e.g. "this is 99.99% gold" vs "this is 73% gold and 27% other things" - you really want to use both techniques. Resistivity/conductivity is about average composition, XRF is about elemental purity.

They have handheld XRF analyzers nowadays. They cost around $20k.

Huh, impressive - I guess I'm out of date (and/or the people I listen to about such things have a working XRF already and don't want to replace a working unit).

You can get a used one for like 3k. I don't really need it but I have it on my santa's list for ages already. One day he will deliver I hope

Interesting. How deep into a gold bar would that work?

Here's a very informative video on this from a 30+ yr COMEX gold trader (the mechanism is discussed from about ~8 mins in): https://themarkethouse.substack.com/p/video-alyosha-with-a-r...

Density, conductivity, x-ray. Density alone won't rule out bars that are spiked with tungsten.

Maybe also moments of inertia?

If the metals were thoroughly combined and met the density equivalent of gold I see no reason why the moment of inertia would not also match that of gold.

Fake with a layer of gold around it has the same moments of inertia.

I love that this question, asked 20 minutes ago on HN, probably been asked on a monthly if not weekly basis by so many people since the invention of gold as currency.

Maybe unrelated to your question, but the individual bars in the Fed vault have specific owners. They are not mingled.

The cheap approach is to check the density - weigh it and measure the volume. But I don't see what the issue would be with melting the gold down to check. There isn't that much of it.

My first guess would be that your gold bar isn't 100% gold, because alloying with a little copper or silver will give you more durable and practical ingot. Ifyou look at a typical gold bar they'll usually have embossed their purity. Even "pure”, 24-carat gold is probably "fineness" 998 or 999, which translates to 99.8% or 99.9% by mass.

I have an auxilary question. Why don't countries have Gold Embassies around the world? Accounts which can be settled in Bulk (e.g. say $100 million gold equivalent size). This way no one country has monopoly on reserve asset.

They do. Countries frequently store gold with trading partners or allies. Germany for instance has extensive foreign gold reserves.

But then the next question is why aren't those used as settlements mechanism?

They are? The issue here is simply that the country thinks there is an imbalance. They can request a in country transfer and do, but in this case it’s not enough.

Because international settlement is huge - something like a trillion dollars a day. (Or maybe that's just currency exchange, which might contain speculation in addition to settlement? Or is that a false distinction?)

Anyway, moving that much gold would be slow, inconvenient, and a significant risk.

Measure its volume by dunking it in a jug of water and compare its weight with its expected weight (depending on the density of gold).

There is a famous tale of Archimedes doing exactly this when posed with the problem of determining if a certain crown is made of pure gold.

Apparently there are bars which are tungsten on the inside. Tungsten has a very similar density.

Presuming you can create an alloy with the same density as gold, I imagined you could also test it's conductivity. I think performing both tests would be enough.

The only metals with which you could make an alloy with the same density as gold, but cheaper than gold, are uranium and tungsten.

Other metals would require too big additions of expensive rhenium/osmium/iridium/platinum to match the density of gold.

The best choice for matching the density of gold is tungsten, but even with that the cost for an exact match of the density would be high. The tungsten objects that are found easily in commerce have a density significantly lower than gold, because they are made from tungsten powder sintered with nickel, not from pure tungsten, which is hard to melt.

The conductivity test is good, but not easy to perform when the object has a complex form. Surface conductivity is easy to measure on any object, but the object could be plated with pure gold, so surface conductivity would show no difference.

For a gold bar of standard dimensions, it should be easy enough to make a text fixture allowing the measurement of the bulk conductivity.

No need for an alloy tungsten will do.

It is rather expensive to make objects of pure tungsten. The tungsten objects that you see for sale are not pure and they have a density more than 5% lower than gold, which is easy to detect by weighing.

Nobody is holding 100% gold. The highest purity is 99.999% and anyone holding that either has an outstanding reputation and XFR scans to back that number or is trying to sell you a lead brick.