W.D.Clinger
Philosopher
In philippeb8's unique world things that are different can have no relationship. Relationships can only exist between things that are exactly the same.![]()
Let's not understate the hilarity of philippeb8's latest howlers.
c, G and c^2/G are 3 different things. The 1st is the speed of light, the 2nd is Newton's gravitational constant and the 3rd is the ambient gravitational potential in the solar system. Thus they have no relation.
Gravitational potentials are negative except at infinity (where they are zero), and the units of a gravitational potential are work per unit mass, e.g. Joules per kilogram, which is m2/s2 when reduced to base SI units.
c2/G is positive and has units of mass per meter, e.g. kg/m.
It is therefore impossible for c2/G to be a gravitational potential of any kind.
Ok then, show the derivation of c^2/G. Thanks.
Hint: constants do not have derivations:
https://en.wikipedia.org/wiki/Einstein_field_equations#Mathematical_form
Maybe that's why GR is not scalable, what do you think?
philippeb8's "hint" links to a statement of Einstein's field equations, which are (with the Misner/Thorne/Wheeler sign and subscript conventions)
Rμν - ½ R gμν + Λ gμν = κ Tμν
where the constant κ isκ = 8 π G / (c4)
With Einstein's original formulation of those equations, a constant was introduced in equations (49) and (50), which express the solution of a differential equation. (philippeb8, of course, may not be aware that solving an indefinite integral introduces an unknown constant or parameter.) In Einstein's 1916 paper, the units of that parameter are length per mass, e.g. m/kg, which is the inverse of the kg/m units of philippeb8's c2/G. It is therefore possible that philippeb8 got his c2/G by combining a misreading of Einstein's 1916 paper with a misreading of the Wikipedia article he/she cited; in what follows, however, I will consider another possible source of philippeb8's confusion.At any rate, Einstein's solution of the differential equations derived within his paper led to the introduction of an unknown parameter. To fix the value of that parameter, Einstein used the technique engineers, scientists, and mathematicians throughout the world use to solve boundary value problems: set the parameter equal to the value that makes the parameterized general solution match a known real-world value at the boundary. In Einstein's paper, that meant the parameter must have the unique value that made Einstein's general theory of relativity coincide with Newton's theory of gravitation in the Newtonian limit. Hence Einstein's equation (69).
That explains how Einstein derived the value of his constant, and it explains how the corresponding constant κ was derived in the modern formulation philippeb8 challenged us to explain.
All that is left to explain is philippeb8's bizarre infatuation with c2/G and his/her belief that it could have anything to do with a gravitational potential. In the above, I mentioned one possible source of that confusion. Another possible source is the so-called Schwarzschild radius
rs = 2 G M / c2
Once again, however, we see G/c2 rather than c2/G. Perhaps philippeb8 just reads these things upside down.