Saying that this is what the formula intrinsically does, amounts to saying that field lines are more fundamental/"real" than action-at-distance forces on point particles.
Yep :-). I don't know enough the physics to back that up, but that's what my gut tells me. A more educated version of me might be able to say something "the vocabulary of forces is 'shallow'; the vocabulary of fields is deeper; the vocabulary of group symmetries is deeper still." I certainly do not have the depth of understanding to make that sort of statement with any authority. If you know enough physics to correct me or clarify, please please do.
why not better go for simplifying Einstein's equation and including 8π in G
If somebody who groks relativity told me that this is the right thing to do, I would believe them (ETA mentioned on Wikipedia). I'd be curious where the factor of 2 comes from in the Newtonian approximation.
I'd be curious where the factor of 2 comes from in the Newtonian approximation.
I can take a stab at explaining this. Both the Poisson equation and the Einstein equation have the general form
In the Newtonian case, F is the gravitational potential. In the Einstein case, it is the spacetime metric. This is a quantity with a simple, natural, purely "mathematical" definition that you cannot play with and change redifining constants; it measures the distance bet...
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