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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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  • Welcome. We deal with mainstream physics here, not so much personal theories. Please take our [tour] and refer to the [help] for guidance as to our ways. Enjoy the site. – Jiminy Cricket. Jan 18 '23 at 08:40
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    You’re mixing up straight paths in space with straight paths in spacetime. For example, a circular orbit in space can be perfectly straight in spacetime. – knzhou Jan 18 '23 at 08:47
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    The definition of a straight path in GR is a trajectory along which your proper acceleration is zero. In flat spacetime this corresponds to our naive interpretation of straight but in a curved spacetime it does not. So the answer to your question is that you have misinterpreted the meaning GR attaches to straight. – John Rennie Jan 18 '23 at 08:54

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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    Your answer is excellent. Free falling objects follow geodesics", which are the "shortest" paths in the relevant geometry, not "straight lines". The fact that in Euclidian geometry geodesics are indeed straight lines is not a sufficient reason to use the expression "straight lines" to mean* geodesics in non euclidian metrics. I have always found this abuse of language extremely misleading. People who claim to be pedagogical and think that describing gravity by "straight lines" is a good idea, are, IMHO, totally wrong. It is maximally confusing for a non specialist. – Alfred Jan 18 '23 at 09:07
  • @Alfred Well, but ... what is a straight line in Euclidean geometry? If you analyze this issue carefully, you'll realize that it is not an abuse of language. – GiorgioP-DoomsdayClockIsAt-90 Jan 18 '23 at 10:15
  • @Giorgiop A straight line is the "path of shortest distance" in Euclidian geometry, and you think it is a sufficient reason to call "path of shortest distance" in non-euclidian geometry a straight line. Let me push this reasoning. A platypus is the only monotreme mammal which is not any of the several kinds of echidna. With your reasoning, a human is a mammal which is not any of the several kinds of echidna. Oh, a human is not a monotreme mammal, but who cares. I decide to call humans platypuses. – Alfred Jan 18 '23 at 19:02
  • @GiorgioP More seriously. The surface of Earth has a non-euclidian two-dimensional geometry. A Tokyo-bound plane starting from Paris starts towards the North-East, flies over the southern parts of Sweden and Finland, enters Russia, flies over the North of Siberia, and finally flies south-east to Tokyo. Is this a straight line (Ignoring the few kms in altitude, it is almost on the Earth surface) ? For you the answer should be YES, since it clearly follows the path of shortest distance to minimise flight time and kerosene use. But who will call this a "straight line" ? – Alfred Jan 18 '23 at 19:27