Large solutions for compressible Euler equations

Geng Chen,

“compressible Euler equations” shows up on the Internet 109,000 places. There are hundreds of variations of that term and related models. I try to find and classify and organize everything on the Internet.

“euler” “compressible” “vacuum” “gravitational” has 134,000 entry points

“euler” “physical vacuum” has 19,000 entry points

I was looking at magnetosonic equations in the limit of zero electron/ion mass ratio. And wanted to see what has been happening in compressible models of the vacuum that might be suitable for checking Alcubierre type faster than light solutions. The magnetosonic models have sufficient flexibility and the “trick” seems to be to not let the magnetic field go to zero.

I have been struck with the exact parallel between the equations for vehicles moving through compressible fluids like air and water. And the same for vehicles moving through the vacuum. The relativistic corrections depend on (V/C) in exactly the same way. The “trick” seems to be to allow that the mass carries stores of energy that can be used as needed. Not just standing outside and throwing things.

At the surface of the earth, the gravitational energy density can be modeled by small particles where the average mass is about 10^-7 of the mass of the electron. That is the mass of a particle, in equilibrium with air at the temperature, whose average velocity is the speed of light. Rather than assign fixed masses to the energy, I am allowing any size fluctuations in a nearly continuous fluid. The scale of the fluctuations sets the kinetic and rotational energies of small regions. Allowing each particle to have magnetic, electric, material and kinetic properties is just a way to allow any model that works to be used and tested.

I studied partial differential equations and compressible fluid flows (aerodynamics) when I was at the University of Maryland at College Park in the later half of the 1970’s. Charles Misner was my academic advisor, but I met Joe Weber (Weber gravitational detectors) and he urged me to study his student, Robert Forward’s, work on combining gravity and electromagnetism into an engineering discipline. Nowadays I call it “gravitational engineering”

For the last 23 years I have been Director of the Internet Foundation. I try to follow all the new technologies in gravitational detectors, simulators and acceleration field generators of all kinds. But mostly I am leaving the problems to the coming generations.

It seemed that you are searching for something. I am reading your papers on ResearchGate (I just “followed” you) and thinking that you can probably understand and make practical contributions to gravitational models. Particularly, you might be able to write down a magnetosonic (call it what you want) model for the gravitational field. It is nearly incompressible and does not reach turbulent states of the vacuum at low velocities. At temperatures near the Hagadorn temperature (you will find it as 155 MeV, but I use SI units for everything, so multiply by the electron charge, then divide by the Boltzmann constant to get about 1.8 * 10^12 Kelvin.) That is where the still smaller particle model of the vacuum can be used, to model the quark gluon plasma. I think of it as the vacuum being a fluid of tiny magnetic particles that can boil at that temperature, form bubbles and shocks and vortices and wakes. The richness of fluid dynamics is needed to describe the wide range of phenomena. A nonlinear Schrodinger soliton has more in common with a vibrating bubble or helioseismology model, than with a Bohr model with idealized masses and fields.

I think you will be rewarded by taking the particle mass down to small levels like that. I personally call those little particles, “gravitons” but keep in mind they are only useful for everyday gravity, and not for inside a Large Hadron Collider or inside a neutron or quark star. I don’t want people to be held up with thinking the universe is forever too far away because the speed of light is fixed and “no one can break the speed of light barrier”. It is just too simplistic models of the vacuum. Clearly the vacuum is an almost perfect superfluid (almost zero viscosity or drag).

Solving the relativistic vacuum equations for a vehicle help to keep the perspective. If you sit outside things, it is much harder to model and change them. So literally imagining a vehicle near the light barrier will help make it easier to keep organized. Anything over 1/10th the speed of light and gravity (GW170817 showed they are identical, not just close, but identical. I used the network of superconducting gravimeters back in the early 2000’s to measure the speed of gravity using the sun and moon tidal signal as an exact reference.)

I have worked on the gravitational potential of the earth for almost five decades now. And I routinely have to take into account the rate of change of clocks over the earth because of the changing gravitational potential from the sun, moon, earth changes, planets and human things. The time dilation equations are identically the Mach equations for a compressible fluid. I can extend that to include time dilation from magnetic, electric and electromagnetic fields now. It is just the corresponding energy density fields acting inside masses of particular density, and having cross-sections and resonances for particular states in the matter used. If it is a car, or bulk material, or biological system, or liquid or anything occupying a volume, it can be scanned for acoustic, magnetic, electromagnetic and kinetic response in 3D as a function of frequency and timing. The reason I am hopeful for “gravitational engineering” is that the sensors and computers are fast enough and low cost enough to measure and control the required fields in real time. And there is enough spare exacomputer time to solve the equations and check it for real problems.

Richard Collins, Director, The Internet Foundation

Geng,

I wrote you an email, but I want you to know I sent it. Check your spam folders too.

I found your paper on “Large solutions for compressible Euler equations” at http://people.ku.edu/~g828c364/application/Euler.pdf and started reading some of your other work. I feel you are looking for something. So I wanted to offer some suggestions.

I have gotten in the habit of posting my messages to people in my personal work area. That is at /?p=1497. If you don’t want me to tell people about your work, just tell me.

“compressible Euler equations” shows up on the Internet 109,000 places. There are hundreds of variations of that term and related models. I try to find and classify and organize everything on the Internet.

Richard Collins, Director, The Internet Foundation