A new way to visualize General Relativity

welcome back to scienceclick today how to

visualize

general

relativity

the objective of this video is to show different representations of the theory and propose a new one that I have not yet found although it has a large number of qualities the idea behind this new representation is to make the best possible use of the video format and in particular its temporal dimension to faithfully reproduce what mathematics tells us. In middle school and then in high school we learned that free fall can be modeled by a force, it is the force of gravity, this force allows us to predict the movement of objects by stating that they attract each other and, in particular, towards each other. massive objects like the Earth.

However, this description is merely an approximation and fails when the attraction is too strong, as in the case of mercury. around the sun it was in 1915 when Albert Einstein proposed a new theory, a rigorous mathematical model that made it possible to describe free fall with greater precision. For Einstein, there is no force that can act at a distance, it is the structure of the universe that distorts and drags objects. towards a fall. To understand this complex theory, it is important to design visualizations that make it more intuitive. The most used representation is that of a large elastic sheet on which massive objects are placed.

By deforming the fabric under their weight, more massive objects attract everything in their direction like marbles in a bowl. At first this image seems to have two advantages, it is very simple and intuitive and it helps us understand that bodies attract each other indirectly through an underlying fabric. space-time whose geometry can be altered, however, although it is very widespread, this way of presenting

general

relativity

has a large number of problems that make it not very rigorous. In this video we will try to improve this image by making four important changes to start the image of the sheet elastic seems to indicate that objects are placed in space-time like marbles, while in reality space-time is the fabric of the universe that contains them, therefore one improvement we can start with is to flatten the objects on the surface so that it is clear that they are not exterior but are contained within space-time.

One of the biggest problems with this representation is that it sort of explains gravity by gravity. To the question why the apple falls to Earth, this visualization seems to answer that This is because the apple is dragged downward, causing it to fall like a marble in a bowl, but it is not acceptable to explain the gravity inside. of space-time using gravity outside of space-time. Therefore, we have to find a better explanation, in particular, it is more rigorous. to say that if the objects follow the well created by the earth it is because they move in a straight line but within a curved geometry when they fall the objects move in a straight line but the curvature of space-time gives us the impression that these trajectories are I understand that we can imagine the surface of a sphere in which two ants would head north at first, the two paths are parallel and we could think that as they move in a straight line the two paths will never intersect, however, the two ants end up meeting in the north. pole this is possible thanks to the curved geometry of the sphere in which straight lines tend to approach each other within space-time the phenomenon is similar and objects appear to attract each other when they simply follow the curved geometry in straight lines however This image of an elastic sheet is still misleading, in fact, one might think that if space-time can bend it is due to the existence of a higher dimension.

Here, for example, the two-dimensional sheet seems to bend towards a third dimension, in reality this is not the case. The case and mathematics of relativity do not require any higher dimension for the universe to bend, therefore it is preferable not to represent this sheet seen from the side but from above with a grid to illustrate the curvature while we are here this also allows us to restore the three dimensions of space in which we live finally the most important problem with this representation is the fact that our diagram completely ignores the dimension of time space-time is an object with four dimensions, three dimensions of space but also one dimension of time that can bend and curve equally faithfully representing a four-dimensional geometry is strictly impossible and therefore we have to find a trick.

A first idea would be to add small clocks to our diagram at each grid point, this way the spatial grid becomes a space-time grid and we understand that time can flow differently depending on where we are, that being said, Adding clocks to our diagram doesn't give us much more intuition, and in particular, we still don't really understand what causes objects to fall if we drop an apple, for example, why does it start moving towards the Earth? To truly understand, it is necessary to remove one dimension of space to represent the dimension of time. In fact, it is the temporal component of the curvature that explains gravity with this diagram. see that the apple is always in motion even when it has no velocity at the beginning of its maximum the apple is still moving in time it moves towards the future when no force is applied to the apple the curvature of spacetime will gradually bend trajectory between a temporal velocity towards the future and a spatial velocity towards the ground, the apple moves in a straight line but the curvature of space-time rotates the orientation of this straight line between time and space, therefore we understand that if the apple falls towards On Earth it is because it started with a velocity through time, the curvature of space-time generated by the Earth has simply converted this temporal velocity into a spatial velocity, having said that as human beings we do not perceive the temporal velocity of objects when An apple is falling and seems motionless to us, we do not perceive the fact that it has emotion through time from our point of view we experience the world moment after moment and this diagram where objects form tubes along time lines of the world is not very intuitive our last step Therefore, it will be necessary to cut this diagram to cut it moment by moment to form an animation that includes time, the curvature of the universe that causes straight lines to plunge into the earth becomes a contraction movement, The speed of this contraction is constant and perpetual because the curvature of space-time which depends only on the mass of the earth is always the same however it is very important to understand that geometry does not really contract, it is the fact that the lines The straight lines come closer together, which gives this impression of contraction.

The phenomenon is quite similar on the surface of a sphere. The curvature is constant on the sphere, but the straight lines seem to be getting closer to each other. It is this representation that I find most attractive to

visualize

the general relativity of the Earth because it is very massive space-time warped giving it a curvature for us the curvature of space-time appears as an endless contraction of the grid in technical terms we say that the volume contained between geodesics contracts with time due to curvature this contracting grid represents what Call inertial frames frames in free fall with respect to this grid, a body that is not subject to any force will retain its motion, therefore , if we let the apple fall with no initial velocity, since no force acts on it, it will remain motionless in relation to the grid, but as the grid contracts the apple will fall.

With this image of relativity it is also easy to see that the surface of the planet it is constantly accelerated upward because it always goes against the natural motion of the grid. Finally, if we throw an object sideways with an initial velocity, no force is applied to it and therefore it will continue in a straight line within the grid, but As the grid contracts, the object is constantly pulled toward the Earth, which is exactly how the Moon orbits the Earth and the Earth orbits the Sun.