https://www.researchgate.net/publication/367280933_The_electromagnetic_self-force_of_a_Lorentz-contractible_spherical_shell_of_radius_R_in_rectilinear_arbitrary_motion_the_terms_of_order_1R_and_R0
Georgeta Vaman,
I found this paper on Arxiv at https://arxiv.org/abs/2301.08223
You might want to post the link or tell ReseachGate where the paper is stored on the Internet. I quickly read some of your older papers, starting with “Cartesian multipole moments and tensorial identities”. I came to your paper following some ideas from “A structure adapted multipole method for electrostatic interactions in protein dynamics” at https://pubs.aip.org/aip/jcp/article/101/1/734/530567/A-structure-adapted-multipole-method-for
I am looking for a way to describe the structure of the gravitational potential at the earth surface at nano and smaller scales. From all indications it is most likely a type of “hyperelastic solid” or “cosmic web”. It is not a continuous field in the old sense, rather a network of dense and rarified parts. Much like the large scale structure of the universe, and much like the pathways for actual energy transfer in real materials like cables, waveguides, wires and real gases.
I won’t bore you with my own interests, but I wanted to say thank you for your work.
When I was reviewing the high harmonic generation papers and groups and methods and devices, they are the ones closest to being able to produce energy densities comparable to the gravitational energy density. On the earth surface that is roughly 380 Tesla or in black body terms, about 1500 eV soft x-ray down through UV. The lightning events on earth are all bounded by the gravitational energy density. As are the magnetic recombination events on the sun.
I was happy to see your use of “infinitesimal charge inside the particle” because that was the only way I found to deal with extended and distorted fields of electrons and particles. The mass of a particle that is in equilibrium with the atmosphere that diffuses at the speed of light is roughly 1 seven millionth the electron mass. It is somewhat artificial, but having a concrete value lets me remember the scale. In practical modeling terms, when 3D modeling inside the electron region, the voxels need to be assigned properties. That can be done by giving all voxels all properties, or by assuming much smaller particles that carry most of the energy density, charge (Joules/Volt), mass and other properties. The cosmic web calculations are highly efficient. I have followed quantum chemistry calculations for more than 50 years now, and in recent years watched closely the methods and successes of the protein model groups as they are sharing and improving the speed and accuracy of molecular models of protein and larger size.
Richard Collins, The Internet Foundation
I found this paper on Arxiv at https://arxiv.org/abs/2301.08223
You might want to post the link or tell ReseachGate where the paper is stored on the Internet. I quickly read some of your older papers, starting with “Cartesian multipole moments and tensorial identities”. I came to your paper following some ideas from “A structure adapted multipole method for electrostatic interactions in protein dynamics” at https://pubs.aip.org/aip/jcp/article/101/1/734/530567/A-structure-adapted-multipole-method-for
I am looking for a way to describe the structure of the gravitational potential at the earth surface at nano and smaller scales. From all indications it is most likely a type of “hyperelastic solid” or “cosmic web”. It is not a continuous field in the old sense, rather a network of dense and rarified parts. Much like the large scale structure of the universe, and much like the pathways for actual energy transfer in real materials like cables, waveguides, wires and real gases.
I won’t bore you with my own interests, but I wanted to say thank you for your work.
When I was reviewing the high harmonic generation papers and groups and methods and devices, they are the ones closest to being able to produce energy densities comparable to the gravitational energy density. On the earth surface that is roughly 380 Tesla or in black body terms, about 1500 eV soft x-ray down through UV. The lightning events on earth are all bounded by the gravitational energy density. As are the magnetic recombination events on the sun.
I was happy to see your use of “infinitesimal charge inside the particle” because that was the only way I found to deal with extended and distorted fields of electrons and particles. The mass of a particle that is in equilibrium with the atmosphere that diffuses at the speed of light is roughly 1 seven millionth the electron mass. It is somewhat artificial, but having a concrete value lets me remember the scale. In practical modeling terms, when 3D modeling inside the electron region, the voxels need to be assigned properties. That can be done by giving all voxels all properties, or by assuming much smaller particles that carry most of the energy density, charge (Joules/Volt), mass and other properties. The cosmic web calculations are highly efficient. I have followed quantum chemistry calculations for more than 50 years now, and in recent years watched closely the methods and successes of the protein model groups as they are sharing and improving the speed and accuracy of molecular models of protein and larger size.
Rather than using just the velocity potential changes, you ought to include the gravitational, magnetic and electric energy density effects. If you multiply 1/sqrt(1 – v^2/c^2) top and bottom by c, you get
c/sqrt(C^2 – V^2) where C^2 is the universal potential (Mach potential) and V^2 is the velocity potential.
To add gravity, you can start with c/sqrt(C^2 – V^2 + 2*Phi_g + Phi_magnetic + Phi_electromagnetic)
Where all the terms are potentials and have units of Joules/Kilogram
The combined “time dilation” from velocity and gravitational potential is widely used for space and gravitational sensor networks. I have been working to include the magnetic effects and electromagnetic effects for the last 42 years or so.
Combining the field for situations where a good approximation is that the magnetic, electric and gravitational energy densities are about equal, lets one convert from one system of units to another and make reasonable estimates of fields, power requirements, power densities and peak fields.
Richard Collins, The Internet Foundation
I am fairly certain that the velocity part of the relativistic effects are connected to the gravitational potential and the potential gradient squared. What I mean by that is that if it is possible to do some of the accelerator experiments in space, there should be a difference. Either in microgravity fluctuation spectrum, or in absolute effects.
The gravitational energy density (g^2/(8*pi*G) = g^2 * 5.96148447E8 kg/(meter^3/second^2) for a field of 9.8 M/S^2 is
(9.8)^2 * 5.96148447E8 = 5.72540968499E10 Joules/meter^3
The magnetic energy density is B^2/(2*mu0) = 3.97887357513E5 (Joules/meter^3)/ Tesla^2
Setting these equal (in equilibrium),
g^2 * 5.96148447E8 = B^2 * 3.97887357513E5
B = g * sqrt( 5.96148447E8/3.97887357513E5)
B = 9.8 m/s^2 * 38.707679678 Tesla/(m/s^2)^2 = 379.335260844 Tesla
I carry full precision through the calculations, so if I have to back up, I can without losing precision. It is a habit that Steve Klosko taught me about 45 years ago when we were working on the NASA GEM series of earth gravitational potentials. Many of the people I met and worked with are gone now. Most were much older than me then.
It is possible to set the value of B numerically equal to the impedance of the vacuum (376.730313668 Ohms) for a particular unique value of the “acceleration at the earth’s surface” That requires some coordinate assumptions and experimental setup but it does make sense if you trace out all the steps.
g_standard = 376.730313668 Ohms / 38.707679678 = 9.73270206 meters/second^2.
In his dissertation, “Detection of Dynamic Gravitational Fields”, Robert Forward starts out with a plea to combine the gravitational and electromagnetic systems of units for practical engineering purposes. It was while I was studying his work and ideas about gravity that I came across the gravitational energy density and usually ascribe it to him. I now know is is much older and deeper, but he was practical and so am I . Precise numbers allow testing, sharing, merging and comparing complex models from many different groups.
The intensity of a wave where the speed is the speed of light can be approximated by
Watts/Meter^2 = (Joules/Meter^3) * 2.99792458E8 Meters/Second
PowerPerUnitArea = (5.72540968499E10 Joules/meter^3)*(2.99792458E8 Meters/Second) = 1.71643464E19 Watts/meter^2
Most of the laser vacuum experiments and laser experiments are still using Watts/cm^2
PowerPerUnitArea = 1.71643464E15 Watts/cm^2
At that intensity there should be some gravitational effects apparent. But the lattice of the gravitational field is extremely flexible and fast. I have been using the term “hyperelastic solid” since it seems to be that kind of cosmic web type structure of interlocking magnetic flux tubes. I think it can be modeled (and the cosmic web) by some fairly simple rules for binding of elementary particles. Those particles will be Fermions because they will have permanent magnetic moments. And there are many electrons intermixed in most materials and air. It has taken me more than 45 years of tedious compiling and checking to learn all the units, all the instruments, all the phenomena, enough to compare.
I am fairly certain that the “quark gluon plasma properties are simply these elementary Fermions. They will mostly bind in pairs to be Boson superconductors. But they can also form chains of arbitrary length, so they can be elementary strings as well.
The reason “strings” has not been getting consistent results is because the arcs joinging the nodes are not uniform in natural materials, but artificial networks where the bonds are KeV and MeV are possible. When I talk about “atomic fuels” I mean the average bonds are in the KeV range up to “nuclear” 2 MeV range. But I think it will emerge as an “atomic fuel industry” that will transform transportation and power.
The strength of bonds in the chains, in the networks, at KeV “atomic” levels rather than 10 eV chemical bond strengths, means that macroscopic materials can be made with strengths a 100 (1 KeV) or 1000 (10 KeV) times stronger than now. I sometimes call those “extended nuclear materials” where whole networks and sheets of nuclear isotopes can join in macroscopic new materials. Or at least in clusters and dense picoParticles. A “nucleus” with atomic mass number of 10^6 should be possible with our current technologies. But if we truly harness these things then kilometers long structures should be possible.
The mass of a particle where the binding energy is the main energy, can be small, even zero. If you look at fusion where the mass of the products is less than the mass of the reactants, the difference in mass is energy as we all know. But more subtle is that the mass that is now in “binding energy form” is NOT gravitational and is NOT kinematic. It is not affected by the gravitational field. We say the mass is less. And we say the energy is negative. I would argue that the negative mass or negative energy is real energy that can be planned for and used, created, packaged, moved, shared, sold and converted to other forms.
Richard Collins, The Internet Foundation
