I was updating my notes of gravimeter arrays as gravitational imaging arrays. At the end I recommend using electrons interferometer and related electron methods for measuring and monitoring acceleration. Every electron on earth has mass and is affected individually by the changing gravitational field. Electron methods are far in advance of atom methods, less expensive usually and more powerful. I have reason to believe that both memory devices (using floating gates) or camera sensors – both have small electron wells, and it is possible to determine very small variations in acceleration from their collective and detailed statistics when the memory is shield or the camera sensor is shielded and darkened. So any astronomical telescope sensor, in dark mode can be used to monitor SOME gravitational signals. A
Any electron device (capacitors and electron wells are the ones I think will be easiest) can be used at any frequency as a gravitational sensor if pushed to “quantum” or “nano” or “pico” levels. I have spent that last few years looking for all of them and there are so many, all I can to is share what I found, point in a direction and keep going myself. Just keep the electron mass in mind. The sun moon vector tidal signal is roughly +/- 1000 nanometers per second squared (nm/s2) at 1 sample per second. After you subtract that, the earth based signals at quiet stations are roughly +/- 50 nm/s2 mostly from atmospheric winds and moisture, earth propagated tides, and many others.
I used the network of superconducting gravimeters over 15 years ago to measure the speed of gravity. Because they are single axis, one sample per second detectors, the precision is limited. I looked for three axis accelerometers sensitive enough to track the sun moon vector tidal signal. In the IRIS.edu seismometer network there are a few broadband long period seismometer where the main part of the signal is the sun moon tidal signal. AND most importantly, it shows that all three axes of the signal only require a linear regression to match to the sun moon signal.
The sun moon vector tidal signal can be calculated precisely using the NASA Jet Propulsion Labs solar system ephemeris which gives the positions of the sun, moon and earth and earth moon barycenter. From these and the latitude longitude and height of the station and its orientation, you can calculate the signal that will be recorded by a three axis gravimeter.
The calculation is the vector Newtonian acceleration at the station due to the sun acting on the station, minus the sun’s acceleration on the center of the earth. Plus the moon’s acceleration on the station minus the moon acting on the center of the earth. To that acceleration vector add the centrifugal rotation of the station around the earth’s axis. The resulting vector, transformed to the station North East Vertical coordinates only requires a linear regression for each axis.
I have a project about this at https://www.researchgate.net/project/Solar-System-Gravimetry-and-Gravitational-Engineering
I also posted some details of requirements for sensor – three axis, high sampling rate (time of flight) accelerometers that can be used in arrays for imaging the interior, oceans and atmosphere of earth. The interior and atmosphere of the sun, and other bodies and targets in the solar system. The reason for time of flight is to allow ease of separation of signals where there are strong magnetic signals, which are nearly indistinguishable from gravity at low frequencies.
Here are some notes at https://hackaday.io/project/164550-low-cost-time-of-flight-gravimeter-arrays That image on the left is one month of superconducting gravimeter data from a station in Japan.
If you look at the image at https://hackaday.io/project/164550/gallery#21f5826751cf7b199a02263bd201e9bb see the cell B2 and B3? Those are the ONLY two numbers you need to fits the theoretical Newtonian vector tidal signal from the sun and moon acting on the station. The multiplier is related to the Lamb number and the offset depends on things like the power at the station, the atmospheric pressure, the magnetic field, and orientation of the sensor. With a three axis, broadband seismometer, they are less sensitive but all three axes will only each require a linear regression (offset and multipler) to fit the station data to the sun and moon signal.
It only requires GM for sun moon and earth, positions of the center of the sun moon and earth over time. Rotation rate of the earth, and geodetic longitude latitude and height of the station,
If you have a permanent station, you can use the residuals from the fit on all three axes to solve for the orientation of the three axes, and allow the location (lat long height) to vary and find the best fit for the station location. This is effectively a “gravitational GPS” and “gravitational compass”
In Aug 2017 the merger of two neutron stars was picked by both the gravitational and electromagnetic sensor networks. They arrived at the same time after a race of 130 Million Light Years. So the speed of gravity and the speed of light are identical. I know of places that won’t be exactly true, but for everyday cases they have identical speeds. It is the speed of light, and the speed of diffusion of the gravitational potential. The gravitational potential of the sun and moon is already at the earth and nearly in equilibrium with the earth’s field at each instant. The changes come at the speed of light and gravity and only at the margin are different.
The Japan earthquake was strong enough that its gravitational potential changes, arriving at both the superconducting gravimeter stations and the broadband seismometer stations, were just barely detectable. At GravityNotes.Org I have notes on the “elastogravity” groups looking at the problem of earthquake early warning, but there are many other groups and ways to tackle that issue.
At the top of the page at GravityNotes.org there is a link (second one) that shows a different station. This is the full spreadsheet to show the regression. I chose this method because it ties the station reading directly to the JPL dataset. It puts the local sensor on an absolute reference frame with the sun moon earth and station gravity comparable across a whole network. It is simple to teach and to calculate. Any group can implement the regressions in small computers directly connected or near the sensor to give absolute gravimeter readings referenced on all three axes.
The signal at a sensitive gravimeter is about 98% sun moon vector tidal signal. The residual (after calibrating to the sun and moon) subtract to get the local effects. Those local effects are mainly atmospheric and ocean, magma, rain, humans. A good sensitive high sampling rate detector can be calibrated from that point by using ocean surface waves, traffic on local highways, and object carefully moved and tracked in the laboratory.
The “game” is to use an an easy model to remove the sun and moon big changes. Leaving all the earth based signals in the residual. Nothing is lost because you keep the raw data. If the algorithm improves and a better “best in the world algorithm” comes up, then you use that, carefully record what you do and ratchet up to a better global sensitivity and cadence.
My goals are three axes instruments (so each individually can be locked to the sun and moon for long times at VLBI accuracies. The statistic get finer and finer. Noting and separating noise sources does two things – it gives you information on new phenomena (rain, atmospheric rivers, winds, ocean waves, rivers, etc etc etc) and it removes those from the baseline sun moon calculations to better match that portion of the signal.
Using “time of flight” or “high sampling rate (MegaSamplesPerSecond = Msps, Gsps, Tsps are all possible) with today’s amplifiers and ADCs and gravimeter designs.
Anything lower than 40 Hertz will be comparable to the size of the earth at the speed of light and gravity.
I am fairly certain that most of the “gravitational” signal is broadband electromagnetic noise. And that it will refract. The gravitational potential and velocity time dilation (or redshift or change in vacuum index of refraction) should apply to the high frequency signals. They are electromagnetic, but it requires dealing with extended electromagnetic sources the size of the earth or sun or some part of them. I have a rough handle on those using methods from statistical mechanics, plasma physics, and many fields. but it is not completely integrated. I have to take each case one by one and figure out how best to deal with the complex signals. There are people better at that, but none of them are working with gravimeter signals on a regular basis (lots of groups I can barely keep up with all the new ones).
So these signals that arrive at the gravimeter station by diffusion of the gravitational potential, will be refracted, reflected, absorbed. They tend to have character much like the wind. Sometimes I think to myself “the local gravitational weather”.
The strain sensors measure the position. The seismometers measure the velocity. The accelerometers, vibration sensors, gravimeters measure the acceleration. The LIGO and Mossbauer detector I think are mostly measuring changes in the local energy density or the local potential field. That is hard to measure. Like measuring pressure. But the acceleration is a force and almost ALL the electronic sensor do a good job with that. The atom interferometer gravimeters could be the best but they usually use vacuum laser and detection methods that are expensive and bulky. The MEMS gravimeters are good for three axis low cost applications – and for stationary or near stationary application an use continuous three axis high samples per second methods to calibrate all three axes to the sun and moon tidal signal. Once earth based sources are tracked continuously then even the local climate models can be used to calculate the spatial and temporal three axis signal that will arrive at each sensor in an array of three axis detectors.
But there are so many groups now. And many devices that are sensitive enough to routinely measure gravitational potential variations – either directly like Mossbauer and LIGO, or by gradients by gravimeter, gravity gradiometer, or tensor detectors (all directions and pairs).
One thing I will keep mentioning is that the best gravitational detector is an electron detector. If you say “electron intererometer gravimeter” that is a real thing. But it is much much too narrow to capture the richness and creativity of what people are doing or could be doing.
The electron is well studied and has a vast array of tools. It has charge for Coulomb fields and force. It has magnetic moment for scattering, formation of superconducting and entangled pairs, for precise frequency measurements and direction measurements. And it has a mass that is nicely tied to the local gravitational potential through the relativistic (velocity and potential) relations. MANY precise measurements of electron transitions – in atoms, molecules, in small floating gate electron wells of memory chips, in the wells of cameras in dark mode, in purpose built arrays and printed antennas – to measure the change in the current is to measure the acceleration.
Since the electron is so versatile and useful, I normally recommend just use an extended framework where you calculate the full Taylor series. Monitor the position (0), velocity (1), acceleration (2), jerk (3), snap (4), crackle (5), pop (6). I did some experiments where I went twenty time derivatives out and there was still data to be found. Crackle is the 5th time derivative of the position, the 4th time derivative of the velocity, the 3rd time derivative of the acceleration. And those data streams are easy to monitor in real time. To correlate, and to share.
Richard Collins, The Internet Foundation