The idea is based on these observations:
•Maxwell I, derived from Biot Savard law and divergece math identities is an analoque to the Einstein field equation relating curvature to mass-energy, i.e they both quantify the magnitude of force/force effect
• Einstein equations hypothesize an underlying gravitational field from which equations of motion detive. Same with Maxwell but with photons
•They both predict ot have plane wave solutions (EM waves and gravitational waves).
Note: While EM waves have been a basis fr commercial implementation, GR grav waves have only bern proposed for scientific utility and canot be produced in the lab.
But is this a final remark or can it be researched more to provide a valid answer?
Dear Philippos Afxentiou Unfortunately our past scientists icons thought and made up one-dimension static equation for three-dimension of nature that is changing constantly. .
To be honest, both did not contribute anything to science.
Cogitate, How could one-dimension equation that does not recognize temperature, pressure,...can describe three-dimension of nature wave that it is chaining with temperature and pressure?
“Is there a analoque,i.e similar conceptual scheme,between Maxwell's and Einstein field equations?... Einstein equations hypothesize an underlying gravitational field from which equations of motion detive. Same with Maxwell but with photons....”
- there cannot be fundamentally some similar conceptual scheme between Maxwell's and Einstein field equations, since classical ED describes the real fundamental Nature Electric force that acts in Matter’s Euclidian spacetime, which is in this case only some “empty container”, where Maxwell’s EM fields and waves are some disturbances in some “Aether” that is placed in the emptiness,
- while the GR equations postulate that the Matter’s pseudo-Riemannian spacetime itself acts on matter in systems “mass-spacetime-mass”; for the same main reason the GR and QM are fundamentally incompatible as well.
So, including, despite that Einstein after 1916 all rest his life attempted “to unite” ED and GR, the attempts failed.
On the other hand yeah, Electric Force, and the really also fundamental Nature Gravity force, in a few traits are similar, and so really scientific classical Gravity Force theory with a well non-zero probability will be in a few traits similar to CED.
Though at that the CED itself really must be fundamentally corrected also, since really it is based on postulate that Electric/magnetic fields are constantly and always radiated by electric charges, and, at that, E/EM fields contain and carry some energy,
- what evidently violates the energy conservation law, the same in fact is postulated in QED.
Correspondingly both - CED [QED also, though ] and CGD really scientific development is possible only basing on the Shevchenko-Tokarevsky’s 2007 Planck scale initial of Gravity and Electric Forces informational physical models, more see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- where, including, it is rigorously scientifically rationally shown, and explained why and how , that these Forces’ fields [and Nuclear force filed, see https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force , all these Forces on Planck scale act by one scheme]
- don’t contain/carry energy, but act in coupled by the Forces systems of particles, bodies, etc.; by using the own energy of the systems’ elements; and only provided this the energy conservation law is valid.
Cheers
There are many ideas and possible solutions to these questions. In my recently publish work on here, Preprint On the Origin and Unification of Electromagnetism, Gravitati...
I tried to reevalute the properties of spacetime itself and was able to (hopefully convincingly) derive Maxwell's equations and field equations for gravitation. I'm aware that the writing style is not always up to scientific standard but I hope I can improve on it in a revised second version later. Please have a look and see if my argumentation can answer your question.
Is there a analoque,i.e similar conceptual scheme,between Maxwell's and Einstein field equations?..Yes, there is deep analogy in derivation of them from principle of least action. I apply some papers.
this has been discussed extensively by Thirring,Friedrich Hund and einstein . have a look at their papers.
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