Gravitational Energy Density, Gravitational Energy, Speed of Gravity, Gravitational Engineering
Chaos in the Cosmos: The mysteries and wonders of gravitation – what truly is gravity? Here’s an attempt to explain! at https://www.youtube.com/watch?v=KaOU8BBlcdw
I suggest you focus more on the gravitational potential, rather than the gravitational acceleration. The acceleration field is the vector gradient of the potential field. And the potential field for the earth, sun, moon, planets — each one of them up close and personal – is known precisely now. There is a “GRACE Follow-on” pair of satellites in orbit that measures the gravitational potential as a spherical harmonic equation calibrated for the earth. It is 2160×2160. And they update the field every month. When you talk about the speed of gravity, it is the same as the speed of light. It is quite easy to measure the speed of gravity now, if you happen to have a gravimeter. 20 years ago there were only superconducting gravimeters that would do the job. Now there are “MEMS gravimeters”, atom interferometer gravimeters, Bose Einstein gravimeters, electrochemical gravimeters, quantum gravimeters, electron interferometer gravimeters and many more. Every few months another one pops up. With data from the JPL Horizon system, some data from the gravimeter networks, you can measure the speed of gravity. It is the same as the speed of light.
When a coronal mass ejection occurs on the sun, the change in the potential takes (right now) just over 503 seconds to diffuse from the sun to the earth. The “gravity”, particularly the “gravitational acceleration” you feel and the little vector tidal gravity effects from the sun and moon, are the effects of the gradient of the potential already around you. That bowling ball on rubber sheet models of gravity are really stupid. They are 2D toy models. Get the real data and plot it as a 3D heat map or particle model for the earth. It is really beautiful. The potential of the earth is small compared to the sun. The gravitational potential at the earth due to the sun is small compared to the contribution to the local potential due to the Milky Way galaxy. Thee farther you go, the more mass there is, and the larger the contribution. When you add up all the potential contributions, it adds up to a number which is the square of the speed of light. The units of potential in the SI system are Joules/KiloGram. You say it “Joules per Kilogram”. The earth’s potential at the surfaces is roughly g*Re = 9.8 (meters/second^2)*6.371E6 meters = 62.4358 MegaJoules/KiloGram. The value of C^2 = (2.99792458E8 meters/second)^2 = 8.98755179E16 Joules/KiloGram = 89.8755179 PetaJoules/KiloGram.
If you think the way I am writing these is a bit odd, it is because these are the Internet standards. Global standards for all fundamental constants, units, dimension, methods, algorithms, all human knowledge. The Big prefixes are capitalized, the little ones are lowerCase. The names of people are Proper to honor them and to make it easier to read.
microHertz, KiloJoule, TeraWatt, picoCoulomb, zeptoVolt. And you have better memorize all of them because on the Internet now all of the prefixes from quecto (-30) to Quetta (+30) If you see anyone using lower case for Big prefixes, slap them.
When the neutron stars collided and merged in Aug 2017, the gravitational potential wave and the electromagnetic wave arrived at earth detectors after a race of about 130 Million Years. That means that the speed of light, and the speed of gravity are identical. Not close, identical. The only way that can happen is if they share the same underlying potential. And it turns out to be true. For many purposes the gravitational and electromagnetic fields serve similar purposes. But the gravitational energy density is so much more powerful than our puny electromagnetic things. The gravitational energy density at the earth surface is roughly equivalent to a magnetic field of about 380 Tesla. The peak of the spectrum of the field here is in the soft x-ray regions, and the only reason we survive is because the effects are so uniform and many and tiny.
The laser vacuum experiments are finally getting to the energy density that matches that. The laser UV and soft x-ray systems that can reach fields of that level (comparable to the gravitational energy density), are producing local combinations of electric and magnetic energy density strong enough to displace the gravitational potential. So as we see more and more “MegaTesla” and “GigaTesla” fields, people will be moving big things around with fields strong enough to perfectly mimic gravitational acceleration fields, and gravitational potential fields. I call that “Gravitational Engineering”. Not floofy theories and thought experiments and endless arguments at things that do not matter. Real things, real systems, real world and heliospheric problems to be solved. And what are the conditions for fusion? Very very close to the conditions for matching the energy density of the gravitational field of earth. So I have been recommending that ALL fusion groups check for the variations in their local gravity. All “quantum computing groups” check their local gravity variations. And of course the laser vacuum experiments. And I suggest the fusion groups think seriously about testing far from earth and far from massive bodies. It is the 1/r^2 acceleration that matters.
IFf you check the earth’s gravitational energy density, it sets the maximum energy density for pair production and gamma rays from the most intense lightning events. On the sun, the gravitational energy density sets the maximum of magnetic recombination events.
If you check the combined gravitational potential and velocity time dilation equation, it has a sqrt(1 – v^2/c^2 + 2*Phi_g/c^2) term. Multiply by C to get sqrt(C^2 – v^2 + 2*Phi_g)
The C^2 is our universal gravitational potential. The v^2 is the velocity potential, the Phi_g is the gravitational potential. And you can add terms for magnet, electric and electromagnetic fields. [ search for “Combined effect of velocity and gravitational time dilation” Wikipedia is horrible about new people destroying what is correct and works. So I hope it stays there. ] If you do GPS/GNSS and satellites, you have to make those kinds of corrections routinely. If you use atomic clock arrays to map gravity and track gravity variations, you have use those kinds of equations. VERY PRECISELY.
Those all have units of potential (Joules/kilogram) and you can add extra terms for the magnetic and electric energy density if you have a mass density to move. It means that you can slow clocks with magnetic fields, And because the effects of magnetic fields are nonlinear at small scales and high field, the core of the gravitational energy density means it is most likely that gravity merges neatly into atomic, nuclear, subnuclear and quark-gluon scale processes — as a single discipline.
Richard Collins, The Internet Foundation
