I’ve heard the term “space time” thrown around, and that gravity “bends space-time” but how does that work?
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People say “space-time” because space and time are not two entirely different things, but two aspects of the same thing.
“Bending” space-time is all to do with geometry. So, the rules of geometry you’re probably aware of are called “Euclidean” after the ancient Greek Euclid. They include rules like: parallel straight lines will never cross. It turns out that you can imagine what would happen if that rule didn’t hold. When you’re letting rules change, you sometimes have to make sure that you’ve got a rigorous definition of what before was pretty obvious, like: what is a straight line, anyway? A good general definition is that a straight line segment is the shortest distance between two points.
The easiest non-Euclidean geometry to imagine is the surface of a sphere, like the Earth. On a sphere, the shortest distance between two points is always a segment of a ‘great circle’, where the equator and lines of longitude are examples of great circles. Airplanes will travel along great circles when they’re trying to minimise the distance they travel between two airports. (Although in practice, they will often not travel on the shortest path for various reasons, but that’s not important here).
Great circles are the analogue of straight lines, but they’re weird. They loop back on themselves. The lines of longitude all start at right-angles to the equator, which you’d assume means they’re parallel to each other, but then they all cross each other at the north and south poles.
The surface of a sphere is an example of a non-Euclidean geometry. Another example is hyperbolic geometry, where parallel lines don’t cross, but they diverge away from each other. This is a lot harder to visualise. People have made video games set in hyperbolic geometries, like [HyperRogue](https://store.steampowered.com/app/342610/HyperRogue/) and [Hyperbolica](https://store.steampowered.com/app/1256230/Hyperbolica/).
What people mean by “bending space-time” is that instead of space-time being Euclidean (strictly speaking it’s ‘Minkowski’ rather than ‘Euclidean’, but that distinction isn’t important right now), space-time actually has a non-Euclidean geometry, and the amount of non-Euclideanness is dependent on how much mass and energy there is.
As previously mentioned, a key aspect of non-Euclidean geometries is what happens with straight lines. Consider this: if an object isn’t accelerating, i.e. moving at a constant speed, then it’s on a straight line through space-time. You can draw that on a graph with time on one axis and position of the object on another to satisfy yourself of that!
So, we expect that if we have two objects sitting alone in space, travelling at the same speed, not accelerating, their paths in space-time are parallel lines. They should stay the same distance from each other. We can tell if they’re accelerating by affixing an accelerometer to each object. Except, we do the experiment, and the two objects will come together, neither recording anything other than 0 on their accelerometers. Because of gravity!
Because they didn’t accelerate, they must both still be going on parallel straight lines in space-time. But their parallel straight lines ended up intersecting! Sort of like what happens with parallel straight lines on the surface of a sphere! What happened is the mass of each object caused space-time to deviate from being Euclidean. That’s what’s meant by “bending space-time”.
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