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I've often heard it said that gravity is not a force, but that massive objects curve spacetime so that paths that look curved are really straight, and what's happening when we "feel gravity" is really just us following straight paths.

.... but ... no. That's clearly not true.

  1. Just because a massive object turns straight paths into curves, doesn't mean I have to follow that trajectory. Let's say there's a "straight path in curved spacetime" from A to B, due to the gravitational effect that B has on A, and I am standing in the middle of that path with zero velocity relative to B. Then I'll still be pulled into B, won't I? That doesn't happen on any other straight path that I know of. So gravity must be a force, it's not just a straight path, since it pulled me in even though I had zero velocity.

  2. Another way to see the above is via the fact that stable orbits are possible. If the Earth moves towards the Sun due to its straight path pointing towards the sun, why does the velocity of the earth in a different direction matter? It should just crash directly into the sun since that's where the straight path is pointing. If you're driving a Bugatti going 300kph and there's a wall "ahead" of you (i.e. on the straight path) ... guess what? You're crashing into that wall.

So no, gravity is not straight paths in curved spacetime. It's pretty clearly a force, since it depends on, and impacts, velocities.

stackoverflowproton
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1 Answers1

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... massive objects curve spacetime so that paths that look curved are really straight ...

I think this is where your misunderstanding lies. General relativity says that objects in free fall (i.e. with no external force acting on them) will follow paths called geodesics in spacetime. These geodesics are the "shortest" path between two points in spacetime, where the distance that determines "shortest" is measured using a particular method or "metric". And the metric in turn depends on the distribution of mass (and energy). So free falling objects follow geodesics and the shapes of the geodesics, which is determined by the metric, are influenced by the presence of massive objects - and this influence is what we call gravity.

In Euclidean geometry straight lines are the paths of shortest distance between two points. So geodesics in spacetime are somewhat like straight lines in Euclidean geometry - but they don't have to be (and usually are not) "straight paths" in space. For example, the orbits followed by planets around the Sun are the spatial parts of spacetime geodesics - the fact that they are curved paths does not stop them being geodesics. When you throw a ball, it follows a spacetime geodesic (if we ignore air resistance) even though its path in space is curved.

It may be best if you forget the "straight paths" analogy and just accept the spatial part of a geodesic can be a curved path in space.

gandalf61
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