I notice this thread comes up when someone searches for gold testing on search engines now. So I wanted to update the thread because I feel there is still too much confusion. Consider what I'm writing here to be said with 100% confidence, and simply study the physics if there is any disbelief.
-Gold dealers have no clue what they're talking about. Reputation is important to decrease the probability of being defrauded, but you should always assume you have received a fake until proven otherwise. I have met at least one vault custodian who spends all his day in the vault and literally has no clue why his testing methodology is flawed. Gold dealers are not physicists or engineers and usually are the type without the mental capacity to understand the physics. I'm sorry that's extremely harsh, but I see all kinds of misinformation and youtube videos on this topic and nobody is doing anything to correct them (the one exception being SilverBullion in Singapore -- they actually have one good youtube video on this topic and they are the only dealers I know who test themselves and do so correctly).
-Buy recent 1 kilogram RCM kilobars if you can, because they are extremely testable by all methodologies I will mention and I have never had any ambiguous results. They have a very smooth back and parts of the front are smooth which allows you get random samples for ultrasound (later). I cannot say the same about other refiners. Maybe others can. Stay the f*ck away from old bars and especially JM.
-XRF (XRay Fluorescence) devices are totally useless for all intents and purposes because they negligibly penetrate the material surface. A non 9999 Au reading will confirm that you have a fake with 100% probability as someone has done a bad job of plating whatever you have, however a 9999 Au reading alone is insufficient. If you don't have access to one of these pricey devices, it is of no consequence to simply skip this test.
-(Prerequisite) Measure the weight using an accurate scale, that is accurate to the 250 milligram, but can deal with 1000g without getting into the nonlinear or damage zone. RCM kilobars are well known for coming out to ~1000.5 grams (your scale should report anything between 1000.0g and 1001.0g). A fake will probably put in too much or too little. This test can give red flag, but otherwise you continue on...
-(First real test) Archimedes density test. You are measuring the buoyancy force of the displaced water after you use string to suspend a gold bar in a tub of water sitting on a scale that has been zero'd before submersion. You can lookup the equations and derive a formula by which the volume cancels out, giving you the ratio of density of the material to water, which you will calculate, and then compare to what gold should be. Even with a cheap kitchen scale, if you can minimize the string used to suspend the bar, you should get to within 5% of the specific gravity and thus density. At this point, you now know that you either have tungsten or some other alloy or non-homogenous combination of material giving the same density as gold, or something that cannot possibly be gold, or something that has tiny air pockets (this was my original concern in this thread, 3 years ago!) but *might* still be gold. I am still not sure if old pouring processes did that, thus why I claim you're best to not risk this and just buy the RCM kilobars if you can.
-(Second real test) Ultrasound + calipers. You can either use an A-line scan device which is just a thickness measurement device usually used for pipes/tracks/etc, or you can use a B-scan defect imager (phased array; same physics as used in medical imaging). The former costs a couple hundred USD on Amazon and the latter will run you between $10k - $120k, yet another reason why I recommend the A-line-based thickness gauges as they will report the first significant reflection. If the material is non-homogenous (tungsten inserts) or homogenous (tungsten, unknown alloy), you are going to know ! If you are very sophisticated, you can attempt to do signal processing on the A-line reflection to determine if any anomaly is something like an air gap. First I start on the backside, set the sound velocity expected to that of gold (3240 m/s) and then measure the reported thickness continuously. The thickness is not constant through the bar, so keep this in mind. What you are looking for is to not see variation by more than 0.5 mm as you move the probe all along the back, left to right and up and down. Then go to the front side. Take all the points without texture that you can. Then measure all of these using calipers. You should be getting the correct thickness to within 0.2mm for RCM bars which is about 2-3% error. Then you can try the beveled parts without too much texture and you should get accurate readings for those spots as well.
We do not know of any material that has the same sound velocity as gold AND the same density as gold. So if you are good so far, then you have real gold. On RCM bars this will have been the case by now. If you are truly paranoid, or got values a little out of the range expected (for example density perhaps within 5% but not 2%, and thickness within 7% but not 3% -- although this already is certainly gold still), you can proceed with one more:
-(Third real test) Through-material conductivity. This is also known as Eddy Current Testing. Recent devices from Sigma claim they get at least a few mm of penetration. The physics suggests it should be on the order of 1 mm, so it's hard to know for sure if they can do what they claim. I believe the truth is about half of what they report in their manual but this is still more than enough to verify deep into gold kilobars (multiple mm on each side). Do NOT use the older devices which produce a weaker field and are only a one-sided coil -- those are surely only giving surface conductivity.
Nowadays many dealers will happily show you the result on their Sigma or use one of the surface wands and leave it at that. That's a good starting point but really make sure you have Archimedes + Ultrasound done, and let the Sigma bulk-ECM (Metalytics Pro SKU only) be your paranoia friend.
In case someone somewhere has figured out how to mimic gold density + sound velocity (not happening), it is certainly the case that mimicing gold density + gold sound velocity + gold conductivity is impossible.
The physics suggests you could also do a heat conductivity test, however I have not yet seen an instrument that can account for the non-rectangular shape of these ingots, so such instrument would have to be 3D-surface aware and complement measurements with model. I have considered developing such a device based on fiducial imaging and thermocouple array and a software that would go with it to compare theoretical to actual, however I am not sure that the market would be big enough for this. If someone has already developed or knows of such a device, I would really like to know more about it please.
I hope this helps someone, somewhere.