Does light always go in straight lines?

The first time I realized that grown-ups were not infallible was when I was trying to find out whether beams of light can bend.

Someone (I don't remember exactly who - either a parent or teacher I expect) told me that light always travels in straight lines. Someone else (another parent or teacher) told me that in fact gravitational fields could cause light bend. They couldn't both be right, so one of them had to have been lying to me. This was a very confusing thing for a young child to understand (not the gravity thing, the grown-ups lying thing) and I vaguely remember being rather upset about it.

I got over it, but it wasn't until I was learning about gravity at university that I found out that they were both right, sort of.

Gravity does affect light - that much has been determined experimentally. I have seen Hubble Space Telescope pictures where a single galaxy seems to appear in multiple places (or is even "smeared out" into a circle called an Einstein ring) due to the light being bent by another galaxy.

But gravity works by causing time and space to be curved in the vicinity of massive objects. What does it even mean for a line to be straight if the space it lies in is curved? It's a similar situation to trying to find straight lines on the surface of the Earth. There aren't any very long ones because the surface of the Earth is itself curved (cue comment about Christian fundamentalists). However, we can find the shortest distance between two points. On the surface of the Earth we can do that by finding a "great circle" (i.e. a circle who center whose radius is the radius of the Earth and whose center is at the center of the Earth) that connects the two points, and following it. That's why the shortest route from London to Seattle goes way up North into the Arctic circle (try it with a globe and a piece of string if you don't believe me).

Similarly, we can find the shortest path between two events in spacetime (such as a photon leaving a distant galaxy and that same photon entering your eye or telescope), even if that spacetime is curved by gravity. Some of these shortest paths turn out to be exactly the paths that beams of light follow. So light does actually follow straight lines with the right definition of "straight", even when it is being bent!

What is even weirder is when you look at shortest paths through spacetime when the thing moving through spacetime is not moving at the speed of light. In empty space, these are exactly the straight lines you would expect. But in a gravitational field, they are curves. In fact, if the gravitational field is large enough in spacetime these curves are parabolas - i.e. the sort of curves you get by throwing some object and watching the arc it makes. Now these are obviously not straight paths in space, but it turns out that they are "straight" paths in spacetime. So now when watching a baseball game you can confuse your friends by saying "my, look at that spacetime geodesic" when someone hits a fly ball.

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