If light has no mass, how does gravitational force bend light inwards

Question

In the case of black holes, lights are pulled into by great gravitational force exerted by the dying stars (which forms into a black hole). If light has no mass, how is light affected by gravity?

In: 784

Answer 1

Have you ever looked at the [flight path of a plane on a flat map](https://previews.123rf.com/images/metelsky/metelsky1911/metelsky191100072/134427430-plane-routes-over-world-map-with-markers-or-map-pointers-travel-by-airplane-concept-flight-path.jpg)? Notice how they all look curved?

At first that might not make sense, because we’re always told that the shortest path between two points is a straight line, so why don’t the planes just fly in a straight line? The reason, of course, is that the Earth is not actually flat: it’s a three-dimensional surface and the map we’re looking at is just a projection of that 3D surface onto two dimensions.

When you look at the flight paths on a globe, you’ll see that the planes are actually taking the shortest possible path *along the curved surface of the globe*.

This is the important thing: what looks like a curved path in two dimensions may actually be a “straight line” (meaning the shortest path) in three dimensions if the 3D surface that the path is drwn on is curved.

According to Einstein, space-time is a four dimensional surface, and when we look at paths in space, we are looking at a 3D projection of the 4D paths that the objects are actually following. And just like the “straight” 3D flight paths that were projected onto a 2D map, when you project a “straight” 4D path onto a 3D surface, it may look curved even though it’s not.

Now light is special: light always follows a “straight” line, just like the airplanes do (the airlines want to spend as little as possible on fuel, so they always take the shortest path).

When there is no matter around, the surface of space-time is flat: there’s no curvature to it in 4D. So the path that light follows when projected into 3D looks like a straight line.

BUT, Einstein says when there’s matter present, the 4D surface of space-time curves, sort of like the surface of a globe. And even though space-time is curved, light still follows a straight line path across the surface. BUT, the path is a straight line **in 4D**. When you project the path into 3D, then it will look curved. But the reason it looks curved is because the path is actually following a curved 4D surface.

TLDR: gravity affects the path of light because it bends space-time.