2] The two 10 MHz reference oscillators are off by 40 Hz then heterodyne together for a beat frequency of 40 Hz. What was 10 Mhz to 10 uHz test is now a 40 Hz to 10 uHz test or 10,000,000.000,010 test to 40.000,010 test.
You are measuring phase differentials - see my post on this earlier - not frequency differentials. those ppb/ppm figures are for long-term frequency stability, not phase stability.
Is this a pipe dream or could it work.
Scientific research is not just trial-and-error. You have to have a theory on why you should expect some differences and then you can design an experiment to show such differences.
Hi Danny
In a mood to write so apologies in advance for longer than necessary answers.
As to frequency vs phase measurement. I hear you. This brings to mind Edwin H. Armstrong inventor of FM radio. His first commercial FM broad cast station starts as a phase modulated signal. This was to have better control modulation by changing the amplitude of 0 phase vs 90 phase . This would then go through several resonate frequency multiplying stages with the end result being a 47 MHz frequency modulated broadcast . This would later become television IF and FM radio pushed up to 100 MHz. From this we could say that the difference between phase modulation and frequency modulation depends only on the period of time the measurement is made. A measurement of 1 cps made in .1 seconds would be a phase difference. A measurement of 1 cps over 10 seconds would be a frequency measurement. A frequency difference measurement to resolve 10 MHz down to 10 uHz would require a measuring time period of 2 days to qualify as a frequency measurement as you rightfully pointed out.
This being said it should be noted that frequency counters have change as technology has advanced. My frequency counter says 400 Hz is 400.000138 Hz with a sample time period of 1 second. How is this possible? Old school frequency counter would say 400 Hz. New frequency counters take advantage of microprocessors to combining both frequency and period measurements and combine these to measurements for best result resolution. The end result is constant resolution regardless of frequency therefore 400 Hz measured over a period of 1 second reads as 400.000138 Hz not 400 Hz. That particular measurement required a 100 second averaging so the real number number is 400.0001 Hz and fluctuating up and down in the 1 mHz range. So close and yet so far.
As to theory and why I would expect an oscillator to have a voltage coefficient frame of reference. When developing a theory there comes a time when the theory starts to write itself. At this point you find yourself in the back seat while the theory drives the car. I have come to personify this theory as Mr VEPS and I can say that his driving skills leave room for improvement , somewhat like a bull in a china shop. However after the pieces are glued back together he is within the limits of empirical evidence. In short it is out of my hands as I am in the back seat at the moment. He is insisting that relative size of a system not the relative inertia will cause time to dilate and that the relative size is changed by charge parity. The only way to remove Mr VEPS from the drivers seat is to test for a small change in time caused by a change in voltage framer of reference , 5 K volts. If it has a negative result I can kick him out of the drivers seat and take back control. If the results are positive I will be stuck in the back seat again. The back seat is not as bad as it sounds. Just sit back and enjoy the ride with no responsibilities.
In summary new frequency counters appear to be within range for this measurement , just in range. The real problem is jitter , hydro hum , IC noise , 5 volt regulators and probably a few more that I am not aware of. And the theory that makes this prediction , bad driver Mr VEPS , is also in place. All that is left is a solid measurement for a thumbs up or thumbs down.