What is the best visual-aide model that most accurately depicts objects moving through warped spacetime?

Question

so far, the best model I've seen, to help me visualize objects moving through a warped spacetime is this video...

A new way to visualize General Relativity.

Is there a better visual representation to more accurately help in understanding better?

Answer 1

tl;dr, General relativity is really hard, you need a lot of visuals; no one visual is necessarily better, they all help illustrate different properties. Use all of them you can, and try to learn some analytical methods if you haven’t so that you have access to more intuition-building diagrams.

Now to dive into it; the answer is a bit complex.

There’s a reason that general relativity has been around as long as it had without any one clear visual taking precedence over another.

The premise of this question is that it is possible to capture a significant amount of the effects curved space time has on a traveling object through curved spacetime.

This is not the case.

General relativity is a theory involving four dimensional space time. Just like anything having to do with higher dimensional objects, it is impossible to completely visualize what is happening in three dimensions. The classic example is a shadow and a three dimensional object. Just how the shadow loses information but contains some about the three dimensional object, so do visual representations of relativistic properties. The best way to reconstruct the original object? Look at many shadows of the same object from different perspectives. So is the same with visualizations; no one model has it all, they all accentuate a different part of a property, and exclude another.

Often times these representations come at a cost. Ideally, you try to make the cost of understanding in a part that you have another model that describes the area well.

This idea of patches of different areas of properties has a geometrical analog that is woven into the fabric of general relativity. One of the base ideas of it is the fact that spacetime is a manifold; a geometrical object that, by definition, cannot be completely described by a representation of smaller dimensional capacity.

Take a sphere for an example; a sphere is a manifold, and there’s a lot of properties of things that can be done on a sphere that cannot be represented with only one two dimensional graph. We’re familiar with this idea in maps; mapping the earth always comes at a cost of information. Normally it’s a cost of correct distances; the top and bottom of the map will incorrectly show distances (for example, Greenland being comparable in size to Australia (Australia has almost 3 times as many square miles). Since no one lives on the poles, the sacrifice of info about them is normally acceptable, and so our models have been adapted. But if we do want to map the poles, we get another map and make the pole the center. What happens then? We lose information about the equator. Hence the idea that no manifold can be completely captured in one snapshot of a smaller amount of dimensions.

Even the video you’ve linked has some issues, and the video creator mentions them. His visual at the end seeks to better show the time aspect of spacetime, at the cost of potentially confusing people that spacetime is actively contracting.

Your best bet is to look at many ‘shadows’ of relativity to better grasp it; both visual and analytical if you can, to get a better picture.

Often times these diagrams are hard to understand, and become especially confusing where relativistic effects are so important that Newtonian mechanics completely breaks down (near the speed of light or near the Schwarzschild radius of an object).

Since curvature is such a general term, each ‘mapping’ of the manifold that is spacetime will be situation dependent, often involving changes of coordinate systems that are essential, but potentially confusing, to remove ‘coordinate singularities’ (an example being the pole on the map; to convince yourself of this, you might ask, ‘what is the longitude of the North Pole?’).

Some different diagrams that have helped many better understand include Minkowski-spacetime diagrams, Penrose diagrams, other diagrams using compactification.

At the end of the day however, these diagrams and visuals make little sense without some analytical background to motivate them. It is very much a matter of asking many questions in each visual, ‘what would happen if something moved from here towards here’, etc. It may seem daunting at first, but with time it will become clearer, and the visuals will begin to open your eyes a bit more.