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Since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts: space, time, and motion. A proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. (Huggett and Hoefer, 2009) [1]. Therefore a better understanding of motion leads to a better understanding of space-time. This is a problem of historical development of science, as product of human scientific practice, subject to future. We use the historical critical analysis of various theoretic proposals in search of clues ignored. “General relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996) [2]. During a time, the declaration of quantum theorists: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996) [2] seemed to solve this problem, but recently achieved with help of the tightly and collectively synchronized clocks in orbit frontally contradict fundamental assumptions of the theory of relativity. These observations clearly disagree from predictions of the theory of relativity. (Hatch, 2004a, 2004b, 2007) [3,4,5]. On the other hand, we are going to show that the prediction of general relativity, that motion occurs in the static gravitational field is not valid because motion always occurs in a given medium as vacuum, atmosphere, water, etc. The concept of motion and the equations of special relativity, general relativity, and Galilee-Newton declare as the elements of motion: mobile and spacetime. In this paper, we present medium (in special, the quantum vacuum), as the third essential element of motion, inseparable of spacetime, since is its material support, and we analyze its consequences in the theories of spacetime. Our contribution is declare, that the space-time itself does not exist, or is a relational property of matter, but a structural property of matter.

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“The question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that the basic principles Einstein proposed are simply incompatible with his theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name general relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say, Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993) [1] . “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996) [2]. During a time, the declaration of quantum theorists: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996) [2] seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradict fundamental assumptions of the theory of relativity. These observations clearly disagree from predictions of the theory of relativity. (Hatch, 2004a, 2004b, 2007) [3,4,5]. The mathematical model was developed first by Grossmann and presented, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann spacetimes. In this article, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch.

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