A new way to visualize General Relativity

[Music] welcome back to scienceclick today how to visualize general relativity the goal of this video is to show different representations of the theory and to put forward a brand new one which i have not yet encountered although it possesses a great 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 in order to faithfully reproduce what the mathematics tell us in middle school and then high school we learned that free fall can be modeled by a force it's the force of gravity this force allows us to predict the movement of objects stating that they are attracted to each other and in particular to massive objects like the earth however this description is merely an approximation and it fails when the pull is too strong such as the path of mercury around the sun it was in 1915 that albert einstein proposed a new theory a rigorous mathematical model which made it possible to describe freefall more accurately for einstein there is no such thing as a force that would act at a distance it is the fabric of the universe itself which gets distorted and drags objects into a fall in order to grasp this very complex theory it is important to design visualizations that make it more intuitive the representation that is most often used is that of a large elastic sheet on which massive objects are placed by deforming the fabric under their weight the more massive objects pull 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 extremely widespread this way of presenting general relativity has a large number of problems which make it not very rigorous in this video we will try to improve this image by making four major changes to begin with the image of the elastic sheet seems to indicate that objects are placed on space-time like marbles while in reality space-time is the fabric of the universe that contains them therefore one improvement that we can start with is to flatten objects onto the surface so that it is clear that they are not exterior but contained within space-time next one of the biggest problems with this representation is that it sort of explains gravity by gravity to the question why does the apple fall on earth this visualization seems to answer that it is because the apple is pulled downwards which causes it to fall like a marble in a bowl [Music] but it is not acceptable to explain gravity inside space-time using gravity outside space-time we hence have to find a better explanation in particular it is more rigorous to say that if 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 objects move straight ahead but the curvature of space-time gives us the impression that these trajectories are deflected to understand we can imagine the surface of a sphere on which two ants would head north at the start the two paths are parallel and we might think that as they progress straight ahead the two trajectories will never cross however the two ants end up meeting at the north pole this is possible thanks to the curved geometry of the sphere on which straight lines tend to get closer to one another inside space-time the phenomenon is similar and objects seem to attract each other when they are simply following the curve geometry in straight lines [Music] however this picture of an elastic sheet is still misleading indeed one could 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 into a third dimension in reality this is not the case and the mathematics of relativity do not require any higher dimension for the universe to bend it is therefore preferable not to represent this sheet seen from the side but rather from the top with a grid to illustrate the curvature while we're here this also allows us to restore the three dimensions of space in which we live [Music] finally the most important issue with this representation is the fact that our diagram completely ignores the time dimension space-time is an object with four dimensions three dimensions of space but also one dimension of time which can equally bend and curve faithfully rendering a four-dimensional geometry is strictly impossible and we therefore have to find a trick a first idea would be to add small clocks to our diagram at each point of the grid in this way the space grid becomes a space time grid and we understand that time can flow differently depending on where we are [Music] 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 to move towards the earth to really understand it is necessary to remove one dimension of space to represent the dimension of time in fact it is the time component of the curvature which explains gravity with such a diagram we see that the apple is always in motion even when it has no speed at the start of its full the apple is still moving in time it progresses towards the future when no force is applied to the apple the curvature of space-time will gradually bend its trajectory between a temporal speed towards the future and a spatial speed towards the ground [Music] the apple moves in a straight line but the curvature of space-time rotates the orientation of this straight line between time and space we therefore understand that if the apple falls towards the ground it is because it started with a speed through time the curvature of space-time generated by the earth has merely converted this temporal speed into a spatial speed having said that as human beings we do not perceive the temporal speed of objects when an apple is dropped it appears to us to be motionless we do not perceive the fact that it has emotion through time from our point of view we experience the world instant after instant and this diagram where objects form tubes over time world lines is not very intuitive [Music] our last step will therefore be to slice this diagram to cut it up instant by instant in order to form an animation which includes time [Music] the curvature of the universe which causes straight lines to dive into the earth becomes a movement of contraction [Music] the rate 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 [Music] however it is very important to understand that the geometry does not really contract it's the fact that straight lines get closer together that gives this impression of contraction [Music] 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 perpetually getting closer together [Music] it is this representation which i find to be the most appealing for visualizing general relativity earth because it is very massive deformed space-time 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 shrinks over time because of the curvature this grid that shrinks represents what we call inertial frames frames in freefall with respect to this grid a body that is not subject to any force will conserve its movement thus if we drop the apple with no initial velocity as no force acts upon it it will remain motionless relative 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 is constantly accelerating upwards because it is always going against the natural movement of the grid finally if we throw an object sideways with an initial velocity no force is applied on it and it will therefore continue in a straight line within the grid but as the grid contracts the object is constantly pulled back towards the earth that's exactly how the moon orbits the earth and the earth orbits the sun [Music] [Music] [Music] you

Channel: ScienceClic English

Views: 1,047,117

Rating: 4.9232574 out of 5

Keywords: general relativity, representation, visualization, grid, sheet

Id: wrwgIjBUYVc

Length: 11min 33sec (693 seconds)

Published: Thu Sep 03 2020

Reddit Comments

[u/Aaron1924]

No need! This video is already awesome!

[u/Adamankhelone]

BONJOUR À TOUS, AUJOURD'HUI DANS SCIENCECLIC

[u/Aquila_Sagitta]

Does this mean that there is temporal potential energy such as kinetic and elastic potential energies of a spring? How would you even go about quantifying that?

[u/Aquila_Sagitta]

What happens to space time at the center of the massive object? Is it just infinitely stretchy and nullifies or something?

[u/ro_hu]

This was interesting. It explains the mechanics of gravity, but I guess I'm still a little confused as to why space-time reacts to matter at all. Like, why is there contraction at all? Why do bodies not just sit in the grid and float, pushing through the space-time like a wind tunnel?

[u/Kidz7708]

I just watched this video yesterday. It does a fantastic job of representing general relativity. The best video I've found yet

[u/Alklazaris]

Finally. I'm getting tired of the cloth representation. Space is more of an ocean than a fabric. Granted water can't compress, but I think I won't get too much hate for it.

[u/abhbhbls]

Wow! This is the first time any of my posts got more than 100 updoots or any award! Thanks guys!

[u/Gnomi55]

Is that the reason why time moves slower when you’re being influenced by strong gravitational forces? Like your speed through time is being transferred into the special dimensions so you’re moving slower through time but faster through space?