Developing a Gravity Industry

Richard Collins, draft 26 Dec 2017

I was going to start with "gravity equals acceleration, the second time derivative of position".  But any real signal ("time series") has first, second and higher derivatives.  The second derivative events are properly what we measure with accelerometers, and the third derivative events are what we measure with LIGO.  That is a rough way to slice things.  Properly, maybe we should be using Taylor series consistently, and look at the full details of every signal.  For practical purposes, for fast computing and ease of use, it is often sufficient to take first, second and higher differences of uniformly sampled real signals, and look at the statistical and time series properties of each.  We have many sparse networks measuring bits of the gravitational field.  I am trying, here, to document them and show how they can be treated as a single gravity industry.  I am also going to document the efforts to generate second and higher derivative signals and use them for practical purposes like manipulation, communication and imaging.

The measurement of gravity/acceleration pervades our society now.  New technologies allow us to use it much like we have used electromagnetism in the past.  So all the things you have done with electromagnetism, think how that might be done with gravity.  The signals from gravity sources are not much damped or interfered with. You can image with gravity signals.  You can signal and communicate with gravity signals.  You can move things with gravity signals.

From the GW170817 kilonova event, the speed of gravity is the same as electromagnetic waves.  The elastogravity experiments show that local measurement of the speed of gravity is possible.  I hope the elastogravity community will improve their instruments, and add speed of light calculations to their routine monitoring.  It will help set a standard for quality and accuracy.

Accelerometers measure acceleration in units of nanometers per second squared, listed as nm/s2 or nm/s^2.  Accelerations associated with acoustic waves in air are measured with microphones.  Accelerations associated with sounds transmitted through the earth are measured with seismometers or geophones.  Accelerations associated with waves travelling at the speed of light are measured with gravimeters.  Since "gravimetry" is ambiguous, "accelerometry" might be preferred.  The acceleration wave travelling at the speed of light/gravity from an earthquake is sometimes called an "elastogravity wave", to indicate it is generated from an elastic event in the earth and travels at the speed of gravity.  Elastogravity measurement are the first experiments on earth showing the speed of light and gravity are likely the same.  We just need accelerometers that can be correlated at high frequencies (GHz and THz and higher) to be able to use these signals for imaging, tracking, and measurement of the earth, oceans and atmosphere.  The photon, atom and electron interferometer-based accelerometers should be sensitive and adroit enough to essentially replicate the full repertoire of electromagnetic techniques at all frequencies.

"Newtonian noise" is the name given, by the gravitational wave community, to the earth-based signals measured by accelerometers, and gravitational wave subsystems.  It is considered by them to be a nuisance.  But for earth-based gravity/acceleration imaging, that is where all the information is kept.  Seismic waves, ocean waves, winds and rain in the atmosphere generate "Newtonian noise" or, preferably, "acceleration signals" or "acceleration waves".

Both electromagnetism and acceleration waves travel at the speed of light/gravity.  They are both waves in the fabric of space.  It is simply sufficient to say they travel at the speed of light/gravity, and say which properties are transported.  Some common transported properties are energy, or momentum, or angular momentum, or linear momentum, or tension, or force, or a very specifically shaped quantum state.  Energy per unit mass is called potential.  Momentum per unit mass is called velocity.  Force per unit mass is called acceleration.  The third time derivative of position with respect to time is called "jerk".  The gravitational wave experiments are tracking third derivative events.  One could also say they are looking for longitudinal waves in the potential itself.  That is much nicer than saying they are measuring jerk events.

The gradient of a potential is acceleration. Measurement networks on earth, and in space, routinely have to correct for velocity and potential that changes the rate of chemical, atomic and nuclear processes.  (I am looking into the effect of the sun moon potential changes on nuclear fission and fusion reactors.)

The "sun moon" signal is the largest, stable, reference gravity signal on earth.  It is a vector acceleration at any location and time.  If it is measured by an instrument attached to the earth, then one must subtract the acceleration of the sun and moon on the earth, since we are presently not able to distinguish the direct signals from the sun and moon.  When we get accelerometers that can detect and record at microwave, infrared and optical frequencies, we should be able to see the unique signatures in the signals from these two direct sources.  For now, we take baby steps and use the low frequency tools that are available.

Sample Excel File of Regression - example of calibrating a superconducting gravimeter station with the sun moon signal.

The sun moon signal varies roughly +/- 1500 nm/s2.  The elastogravity signals range +/- 1 nm/s2.  The earth tide signals are +/- 20 nm/s2.  Movements in the atmosphere are in the +/- 5 nm/s2 range.  Polar motions 1 nm/s2.  

A kg man at meters is Gm/r^2 =   pm/s2 (picometers per second squared).

A kg ocean wave at meters is   pm/s2

A kg 747-100 at meters is   pm/s2

An earthquake of moment magnitude at a distance of km, of shear modulus MPa, and density kg/m3. If the average slip is meters, and the volume of the slip is m3,   pm/s2

The sensitivity and sampling rate of an instrument determines what can be seen by the instrument.  I am not an expert of all the types of instruments in use now.  I do think that there needs to be a better reporting of sampling rate, bits per sample, energy per unit range, statistical summaries of real signals, and much much better sharing of signals.  It is too expensive for everyone to build LIGOs, ring lasers, gravimeters, VLBI networks, precise GPS stations, nuclear reactors and such - all of which are affected by gravity.  But it cost little to share signals on the Internet.

Taylor Series, Accelerometer,

The study of acceleration waves is also the study of transmission of acceleration at the speed of light.  When we learn to do this well, we can go back and reexamine how our electric and magnetic fields are just ways of expressing the transmission of forces at the speed of light/gravity. 

The energy density of the gravitational field is very high.  When we can routinely synthesize acceleration fields, either equilibrium or dynamic ones, we will also have effective control of gravity.

The signals from a seismometer are usually reports in velocity units.  The signal is proportional to the instantaneous velocity of the mass.  We take one time derivative to get a signal that will correlate with the true acceleration.  In an atom interferometer and many other experiments the signal is proportional to a distance, so we take the second time derivative to get a signal that will correlate with the true acceleration.  This is how you use the sun moon signal for calibration.  What I have found is that it is not necessary to convert instrument voltages and currents to position measurements.  It is only necessary to take the first and higher derivatives, correlate with the sun and moon signal, then you have a workable calibration without having to worry about the detailed steps.  If you have the leisure to work out the fundamentals, great.  But otherwise you can get something that works and tackle harder problems like imaging or manipulation.

If you use a tiny accelerometer to measure the motions of a small magnet, then randomly generate magnetic fields with an array, you can correlate the motions of the magnet with signals generated, and converge to a control signal to move the magnet at will.  Yes, it is a lot of data, and you have to collect data within the time frame of the motion of the mass, and the signal generating time, and the propagating and response times, but it can eventually be made routine.  We can start with the base solution, calibrate locally, then move things at will.  If it produces an acceleration, it is gravity.  Keep it simple.