Originally Posted by **avito009** It is really simple putting 2 + 2 to get 4. The Danish astronomer, Olaus Roeme in 1676, first successfully measured the speed of light. So it was not einstein who measured the speed of light.
So the logic is simple see when it was proved that gravity is a fictitious force by equating the two equations F=ma and universal law of gravitation. So gravity formula was F=ma. So what does that prove? It proves that there has to be a constant motion in a straight line.
Straight line by observing when you throw a ball in air vertically it falls down in a straight line. Will get back to this later on. Now constant speed: When can there be a constant speed it can only be there if acceleration is zero. |

I'm not trying to get on your case or bury you with notation but I don't think you are truly appreciating the complexities here. So...

The Einstein field equations in GR are as follows:

$\displaystyle R_{\mu \nu} - \frac{1}{2} R~g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{ \mu \nu}$

I'm going to ignore T, the energy-stress tensor in what follows. (That means there's no mass in the region I'm defining but mass is somewhere in a larger space.) For convenience as well as the fact that I'm not terribly comfortable with it.

The scalar curvature is

$\displaystyle R = R^{\mu}_{\mu}$

and the Ricci tensor is

$\displaystyle R_{\mu \nu} = R^{\kappa}_{ \mu \kappa \nu}$

and the Riemann tensor is

$\displaystyle R^{\alpha}_{\beta \gamma \delta} = \Gamma ^{\alpha}_{\beta \delta,\gamma} -\Gamma^{\alpha}_{\beta \gamma , \delta} + \Gamma^{\mu} _{\beta \delta} ~ \Gamma ^{\alpha}_{\mu \gamma}

- \Gamma ^{\mu}_{\beta \gamma} ~ \Gamma^{\alpha}_{\mu \delta}$

and the connection is

$\displaystyle \Gamma ^{\alpha} _{\mu \nu} = \frac{1}{2} g^{\alpha \delta} \left ( \partial _{\nu} g_{\delta \mu} + \partial _{\mu} g_{\delta \nu} - \partial _{\delta} g_{\mu \nu} \right ) $

where $\displaystyle g_{\mu \nu}$ are the components of the metric. (I hope I've got all the components right!)

The topic drives even the relativists nuts sometimes. The base of the derivation of the field equations comes from principle of equivalence, which is very simple but there's really not much simple about the field equations.

-Dan

PS Gravity is not a fictitious force. We can look at it from the standpoint that gravitational force is nothing more than a bunch of equations that mimic the non-Reimannian structure shown above or we can say that matter actually bends space-time. This is an ongoing Philosophical topic.