I think you are probing beyond the envelop of the state of the art measurement technology that mankind has to offer now.
Hi
That just isn't true.
The initial statement wants to look for a 1x10^-12 frequency change. You can buy OCXO's on eBay that will have ADEV's in the 1x10^-13 vicinity. Those OCXO's were measured with very normal test gear. It is specialized gear, but it is not "un obtainable". The nice thing about the measurement gear is that it generally gets more accurate the longer the measurement. Something that does 1x10^-10 at 1 second (like a HP 53132) will do 1x10^-12 at 100 seconds or 1x10^-13 at 1,000 seconds. If you go with a 5370 or an SRS620, you start at 2x10^-11 and go from there. There are a *lot* of measurement techniques out there. NIST has very little doubt they can measure frequency down to 1x10^-15.
If you do as suggested in another post, take the voltage up from 5KV. That's quite do-able with a variety of gear. It is not gear I have siting here in the family room. It is stuff you can buy. 60KV was suggested. 100KV might be equally easy. Gear that went way above that was state of the art in ... errr ...1890. Having worked with one of those big old beasts, no I would *not* do it like they did it "back in the old days".
With a voltage of 100KV, you move your delta F up by a factor of 20. Now you are looking for 2x10^-11 and not 1x10^-12. That's frequency counter territory.
Do you want to do this as an AC measurement? Sure. Voltage up / voltage down / repeat is the way to do it. Maybe you can sweep in 10 seconds, maybe it will take longer to do a sweep. Monitor the frequency and the voltage. Look for a nice clean correlation. Keep things running for a few thousand cycles. Pile the data together and you have pretty good confidence.
The problem with this (looking at it as a sceptic) is *not* running the experiment. By the cost measures of modern physics, the cost to do this isn't even round off error. The problem is doing it in a way that proves what you find beyond any reasonable challenge. The test gear and OCXO's can do itheir part.
Bob