Is General Relativity a Euclidean?

A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.

What geometry does General Relativity use?

A version of non-Euclidean geometry, called Riemannian Geometry, enabled Einstein to develop general relativity by providing the key mathematical framework on which he fit his physical ideas of gravity.

Why do we need non-Euclidean geometry?

The philosophical importance of non-Euclidean geometry was that it greatly clarified the relationship between mathematics, science and observation. The scientific importance is that it paved the way for Riemannian geometry, which in turn paved the way for Einstein’s General Theory of Relativity.

Is relativity a non Euclidean?

A non-Euclidean universe was too strange for many to accept at first. Yet it was non-Euclidean geometry that paved the way for Albert Einstein’s theory of general relativity in the early 1900s and the modern understanding of space-time.

Is General Relativity non-Euclidean geometry?

Does the general theory of relativity contradict Euclidean geometry?

So, what we see here in the case of the general theory of relativity is not that it refuted euclidean geometry. Euclidean geometry itself does not contradict non-euclidean geometry, because an euclidean space is one of an infinity of possible spaces.

Is Euclidean geometry valid and consistent?

In fact, in this new scenario euclidean space became one of an infinity of possible mathematical spaces. It did not refute at all that in euclidean space the sum of the angles of the triangle is 180°, or that the Pythagorean Theorem is true. What it did refute was the belief that the only valid and consistent geometry is euclidean geometry.

What is the history of non-Euclidean geometry?

It was not until János Bolyai (1802-1860) and Nikolai Lobachevsky (1793-1856) that a variant of non-euclidean geometry called “hyperbolic geometry” was developed, which was ignored and rejected by most of the other mathematicians at the time for being counterintuitive.

Should mathematics be revised in light of empirical discoveries?

One of the most cited arguments in favor of revision of mathematics in light of empirical discoveries is the general theory of relativity and its adoption of non-euclidean geometry.