Thanks Alpha, my purpose is just to understand better the Relativity and stimulate reflection.
Part of getting to understand relativity, or anything really, is finding things out about it before you start dismissing it. As you've shown, many of the 'problems' you claim exist in relativity are artefacts of either you not understanding it or because you have a pre-existing bias.
In a video (in Spanish) Carl Sagan says that the curvature of space-time is a dimension that is created (5D).
I would like to know your opinion about it.
URL of the video:
http://www.youtube.com/watch?v=VKhOhHWP6Lc
I don't speak Spanish so can't say anything about what Sagan does or doesn't say. However, curvature does not add dimensions. That isn't what general relativity is about, something you should have found out about already. Suppose there's 3 dimensions of space and 1 of time, giving 1+3 dimensional space-time. If such a space has zero curvature, it's just flat, then the metric is $$\eta = \left( \begin{array}{cccc} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right)$$, ie the space-time interval is $$ds^{2} = \eta_{\mu\nu}dx^{\mu}dx^{\nu} = \left( \begin{array}{cccc} dt & dx^{1} & dx^{2} & dx^{3} \end{array}\right) \left( \begin{array}{cccc} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right) \left( \begin{array}{cccc} dt \\ dx^{1} \\ dx^{2} \\ dx^{3} \end{array}\right) = -dt^{2} + (dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$. Curved space-time is then just allowing the entries of $$\eta$$ to become general functions, which together must satisfy the Einstein Field Equations. For example, the Schwarzchild black hole metric is $$\eta \to g = \left( \begin{array}{cccc} -\left(1 - \frac{2M}{r}\right) & 0 & 0 & 0 \\ 0 & 1 - \frac{2M}{r} & 0 & 0 \\ 0 & 0 & r^{2} & 0 \\ 0 & 0 & 0 & r^{2}\sin^{2}\theta \end{array} \right)$$. Curved space-time (though it technically has zero Riemannian curvature) but still in 4 dimensions.
Curved space-time isn't space-time which curves into extra dimensions, the pictures seen of a ball creating a 'pit' in space-time are metaphorical, they aren't accurate representations of what GR says about gravity. Curved space-time is when lengths of rulers start stretching and shrinking. A clock on a satellite will tick faster than a clock on the ground, the 'ruler of time' has been warped.
2 - The curvature of space-time. (weakness)
Why is that a weakness? In fact it means you can put gravity on the same mathematical footing as the electroweak and strong forces (gauge theories). In quantum field theory the field strengths are actually curvatures of an abstract space known as a gauge bundle. In general relativity we have the Riemannian curvature tensor which is, unsurprisingly, the curvature of an abstract space known as a tangent bundle.
3 - The gravity force doesn't exist. (weakness)
This is more of a philosophical interpretation.
