# Distorted Universe: From Euclid to Einstein through Plato

How to detect what you cannot see, what does not emit light of any kind, neither of which our eyes see, nor infrared, nor X-rays, …? How to detect the dark matter black leg, the exotic, the one that we astrophysicists like but nobody finds in a laboratory?

An answer was given to us by a certain Albert Einstein more than a century ago, with the so-called General Theory of Relativity. More than 100 years later, this theory will be the basis of a space mission of the European Space Agency, known as Euclid. With this telescope, and applying what Einstein taught us, in the next few years we want to make a highly accurate map of all the matter and energy in the universe.

The Euclid mission owes its name to one of the Greeks who still has the most influence in our education and in our minds today. If we want to go from home to the bar across the street, oh those bars! How do we plan to do it ?: in a straight line, which is the shortest distance and the fastest way to meet friends and have a drink as soon as possible. Two parallel lines never intersect, they also teach us that from a young age. Well, those two and three other statements are the basis of what was known as plain geometry for almost two millennia, but today we call Euclidean geometry. The Greek Mathematician Euclid wrote in his work “The elements”Much of the notions of geometry that we all have in mind today, starting only from those 5 axioms or pre-assumed statements (therefore, not proven) and showing, based on them, for example, that the sum of the angles of a triangle gives 180 degrees or the famous Pythagorean Theorem. Does it ring a bell? Irrefutable truths, right?

Today we know that the geometry of spacetime on a small scale is not flat, spacetime curves

In the nineteenth century, geometry underwent such a revolution that it was necessary to give a surname to what until then had been considered irrefutable truth, which was renamed Euclidean or plane geometry, because much of what Euclid described refers to geometric shapes. in a plane, such as triangles or parallel lines. We learn about it in school.

Today we know that the geometry of spacetime on a small scale is not flat, spacetime curves. As a consequence, the light rays do not follow straight lines but what are known as geodesics. And also as a consequence, the angles of a triangle do not have to add up to 180 degrees. It is easy to check. We can form an imaginary triangle by “walking” across the earth’s surface. We started walking along the equator from, say, the vicinity of Macapa, in Brazil, until we find the African coast more or less in Libreville, Gabon. We then turn 90 degrees to the left and walk straight, which means that we are moving along a meridian to the north. We arrive in Europe, we will pass near Milan, Italy, and continuing with our imaginary walk we will arrive at North Pole. There we turn about 96 degrees to the left (around 8, they would say at films) and we walk in a straight line again, following another meridian that will take us back to South America, passing near Medellin, Colombia. When we meet the equator, we turn left again 90 degrees and arrive at the same place where we started our journey. We have formed a triangle on the earth’s surface. And the angles add up to 273 degrees, not 180 degrees. The surface of the Earth is not flat, it is an example that there are more possible geometries than Euclidean and the same could happen with the universe, but in 3 spatial dimensions and a temporal one.

We return to the Euclid mission. And we appeal to another philosopher: Plato. Is famous the allegory in which some prisoners locked from birth in a cave only have information from the outside through the shadows that are projected on the wall, deformed and with an appearance largely due to a bonfire that projects its light on real objects. We too are prisoners from birth, we don’t know what the universe is like in detail, and we try to know it through the light that comes to us from the galaxies. Rays of light from distant galaxies have to pass through spacetime curved by matter in their path. The result when we collect photons from those distant galaxies with our telescopes is that we see the deformed galaxies, not what they really are. We could compare this phenomenon with a fountain full of water, with coins scattered around its bottom, as if it were the Trevi Fountain (more memories of those trips !; and when coins could be thrown into the Fountain!). If the water moves, however transparent it is, we will see the deformed coins.

The Euclid aims to make a map of all the matter and energy that make up the universe, both the visible and the one that does not emit or interact with photons

This is where the power of the physics and mathematics of Einstein’s Theory comes into play. Studying the deformations of galaxies we can know the matter (and energy) content of the universe, which is responsible for the curvature of space-time and the consequent deformation of the image of galaxies. The thing would be conceptually easier if we knew what galaxies are really like, if someone could come out of the prisoner cave and see reality as it is. That is not possible, strictly speaking. In addition, the distortions that form in the image of the galaxies are extremely small, the coins practically look the same in the source analogy. And, as if that weren’t enough, galaxies have evolved in shape (like coins!). Studying as many galaxies as possible, in all directions that we can, at different distances, what Euclid intends is to make a map of all the matter and energy that make up the universe, both the visible and the dark black leg, the one that does not it emits or interacts with photons, we cannot see, nor have we ever detected directly, but it is the most abundant in the universe! But it curves space-time.

Euclid se will launch next year, if all goes well, and it will be collecting data for more than five years. When he finishes his mission we will have a better understanding of the components of the cosmos and how Euclidean or curved the universe is on a small and large scale. Euclid will be like the prisoner who comes out of the cave and then recounts to others what reality is truly like. I hope we do not deny your discoveries and matemos, although denialism (and the Dunning-Kruger effect) is in vogue.

**Pablo G. Pérez González*** He is a researcher at the Center for Astrobiology, dependent on the Higher Council for Scientific Research and the National Institute of Aerospace Technology (CAB / CSIC-INTA)*

**Cosmic Void*** It is a section in which our knowledge about the universe is presented in a qualitative and quantitative way. It is intended to explain the importance of understanding the cosmos not only from a scientific point of view but also from a philosophical, social and economic point of view. The name “cosmic vacuum” refers to the fact that the universe is and is, for the most part, empty, with less than 1 atom per cubic meter, despite the fact that in our environment, paradoxically, there are quintillion atoms per meter cubic, which invites us to reflect on our existence and the presence of life in the universe. The section is made up of ***Pablo G. Pérez González***, researcher at the Center for Astrobiology; ***Patricia Sánchez Blázquez***, Professor at the Complutense University of Madrid (UCM); and ***Eva Villaver***, researcher at the Center for Astrobiology*

*You can follow MATTER in** Facebook**,** Twitter** e** Instagram**, or sign up here to receive **our weekly newsletter**.*

Reference-elpais.com