#### Double Pendulum Interferometry DPII

Bepi

The objective here is to explore the possibility of measuring something useful by correlating period fluctuations between two clocks.

Hence the second I in the name of the proposal, DPII, which stands for intercontinental under my, possibly wrong, assumption that the most likely source of uninteresting correlated signal comes from weather fluctuations, temperature and pressure, and that these are least correlated if the two clocks are as far from each other as possible.

What is correlation analysis is well described elsewhere and is in widespread use in all sciences but not only, in finance for example, notably in high frequency trading.

I have mentioned correlation loosely, I have in mind mainly frequency domain analysis but the time and frequency domains are informationally equivalent and one can go from one representation to the other depending on need. For reference one can read Wikipedia under Cross-correlation, other relevant keywords are Cross-spectrum, Cross-phase and Coherence.

For example if we take as a first objective the one of measuring the longitude difference between the two locations of the clocks through gravity fluctuations linked to the earth rotation, the frequency domain is the one to use and the relevant quantity is the cross-phase between the two signals at the relevant frequency.

The accuracy of the measurement correlation, the functions to correlate here are the two period fluctuations vs time, depends crucially from the length of the time series. An important subject to discuss will be: how long can we, or want, to take the record of a clock ticking for.

Once the measurements are taken correlated stuff might, or might not, appear out of the noise, if it does the more fun subject of discussion will be its origin.

My personal proposal would be to start with simulations on signals we have some experience about, clock noises (among the uncorrelated) and tidal forces (correlated but out of phase), with the double scope of learning how to use the necessary algorithms and discovering if this is a worthwhile exercise or not. At least in theory.

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Bepi

Harvey Moseley

Hi Bepi,

I would guess the widely separated clocks will be uncorrelated, but if you had a nearby clock (same building, same town, same country) where atmospheric pressure and temp are correlated, you would expect the much higher correlation.   Also, if you record the data using  high quality sampling clocks, the comparison should have little error associated with it, only the errors of the pendulums, which we want to see.  On the other hand, since these perturbations due to temp. and press.  are small, we would expect largely linear dependence on them, so a first very interesting test is to correlate out these two important parameters and see what the characteristics of the residual noise is.
Very interesting.

Best,
Harvey

On Fri, Jan 24, 2020 at 7:38 AM Bepi <pepicima@...> wrote:

The objective here is to explore the possibility of measuring something useful by correlating period fluctuations between two clocks.

Hence the second I in the name of the proposal, DPII, which stands for intercontinental under my, possibly wrong, assumption that the most likely source of uninteresting correlated signal comes from weather fluctuations, temperature and pressure, and that these are least correlated if the two clocks are as far from each other as possible.

What is correlation analysis is well described elsewhere and is in widespread use in all sciences but not only, in finance for example, notably in high frequency trading.

I have mentioned correlation loosely, I have in mind mainly frequency domain analysis but the time and frequency domains are informationally equivalent and one can go from one representation to the other depending on need. For reference one can read Wikipedia under Cross-correlation, other relevant keywords are Cross-spectrum, Cross-phase and Coherence.

For example if we take as a first objective the one of measuring the longitude difference between the two locations of the clocks through gravity fluctuations linked to the earth rotation, the frequency domain is the one to use and the relevant quantity is the cross-phase between the two signals at the relevant frequency.

The accuracy of the measurement correlation, the functions to correlate here are the two period fluctuations vs time, depends crucially from the length of the time series. An important subject to discuss will be: how long can we, or want, to take the record of a clock ticking for.

Once the measurements are taken correlated stuff might, or might not, appear out of the noise, if it does the more fun subject of discussion will be its origin.

My personal proposal would be to start with simulations on signals we have some experience about, clock noises (among the uncorrelated) and tidal forces (correlated but out of phase), with the double scope of learning how to use the necessary algorithms and discovering if this is a worthwhile exercise or not. At least in theory.

--
Bepi

Bepi

Bob Holmstrom wrote on a different thread where this subject surfaced originally:

Detecting ‘earth tides’ (variation in gravity due to the moon and sun) is not an easy task.  I am not aware of any Syncronome (other than Shortt versions) having achieved that goal.

I naturally agree with his statements but I want to point out to a couple of reason why it seems to me worthwhile insisting with the potential of regular room pressure synchronomes in this field. Not by chance both reasons are linked to advances of digital computing.

One is that since we are not measuring time here but gravity we can pick the periods we want to do this measurements, in particular we could use only the free pendulum periods, and among those the ones farther away from impulsing. This is in itself interesting because allows experimentation with clocks of all ages, makes and state of tuning.

The second one is the correlation technique which could take care precisely of the hardest to duplicate improvement which distinguishes the advanced clocks from the others. Vacuum vessels where installed to avoid air density variations, temperature is easier to compensate, with a thermostat.

Reducing the pressure to 5% of the atmospheric, like in the Shortt, would be advantageous in itself because of the pendulum Q increase, but not so dramatic in noise reduction. A factor of 3 or so in regularity? Correct me if I am wrong, I never had the time, nor the long term data, to check noise spectra at the very low frequency we are interested in.

Back of the envelope calculations for the correlation, assuming the weather in the two very far away places is completely uncorrelated, could reasonably account for a factor 100 improvement. I am counting on the good will of the doldrums.

Harvey, I see what you mean. Isn't it what we are already doing though? By measuring temperature and pressure with specialized instruments which are free of the clock noise. Conversely we could correlate the predictions of the astronomical gravity fluctuations to find out the clock noise but it wouldn't be instrumental, it could if we could use a precision gravimeter. I don't know anything about gravimeters in practice though.

It's not just tides, I am curious to see what the correlated "residual" is, it might be non trivial. Maybe even weather wise.

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Bepi

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