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True gravitational force is something that can’t be transformed away by an arbitrary choice of frame (even an accelerating one). As a brief example, consider t

True gravitational force is something that can’t be transformed away by an arbitrary choice of frame (even an accelerating one). As a brief example, consider two objects in downwards free fall toward the centre of some massive object. Since they head towards the centre, in a free falling frame the two objects actually get closer to each other until they collide as they reach the centre. This is known as the tidal effect of gravity and is the actual physical content of general relativity. This effect can be shown to be obtained by an appropriate curvature of spacetime which itself can be shown to be related to the stress-energy of matter inhabiting spacetime.

freshhawk 6y ago
"If you and a friend started walking straight north, both at the equator but a long distance apart, you would gradually get closer to each other until you collided at the north pole." I always thought that was a nice way to drop one dimension down to get the intuition. To the metaphorical 2D ant they see two friends attracted to/falling towards each other, but they are going in a straight line on a curved surface and there are no forces at play.
rokobobo 6y ago
It's been some time since I studied these things, but I believe the post was trying to illustrate that the geodesic lines in spacetime created by Earth's gravity field can be visualized as straight lines after a nonlinear change of the coordinates system. [1] To simplify, these are the lines along which particles move when no outside force is exerted on them--again, considering gravity to be a distortion of spacetime and not a force, very much like the well-known metaphor of steel ball on a rubber sheet, which would curve marbles towards the "well" it's created in the sheet. But you're right that once the marbles and the steel ball get to a point where one of the gravitational fields cannot be ignored, this framework becomes less useful. [1] https://en.wikipedia.org/wiki/Geodesic https://en.wikipedia.org/wiki/Geodesic
dreamcompiler 6y ago
I take your point, but I think the author's main point was that because objects in free-fall merely follow spacetime geodesics, it makes calling gravity a "force" a little bogus, at least compared to the other forces. Tidal effects don't change that; tidal effects mean the spacetime curvature "over here" is different than the spacetime curvature "over there", which means the principle of equivalence isn't true in a global sense. But objects still follow spacetime geodesics, which is a concept that's hard to reconcile with the notion of a "force."
- jiggawatts 6y ago
  That "perspective" can be extended to other forces. E.g.: one could say that an electron taking a complex spiralling path through a magnetic field on Earth is merely following a "gravity+EM geodesic" and is actually in free fall the whole time.
didibus 6y ago
I'm super layman in all this, but I think the word force here refers to the Newton's force. Which experimentally was shown to not properly predict the effect of gravity, where as seeing gravity as a distortion of spacetime instead of as a acceleration force applied to the objects, did predict accurately the trajectory in experiments. You can call both a force in the generic dictionary definition of force. Because obviously it's crazy that something can be so powerful as to distort spacetime itself. But gravity wouldn't be a force in the Newton sense of being something that affects the acceleration of an object.
- Smaug123 6y ago
  If you choose to view the universe in one particular coordinate system (e.g. one centred on your eyes), then you'll see some things mysteriously happening. For example, you might find that if you release something from your hand, it will mysteriously move towards your feet. Eventually you'll realise that a bunch of things can cause things to mysteriously move, and you'll start using the word "force" to describe "tendency to mysteriously move". But some of these forces are not observed by other people who are watching; they arise as by-products of the fact that you are the one doing the measuring. For example, if you're falling in a lift, you won't observe the force that causes a ball to fall towards your feet; but I, standing on the ground outside the lift, will observe that actually you and the ball and the lift are subject to this force. In fact there's an underlying reality which we can't directly observe but which we can infer from the paths of objects. That reality is a curved spacetime, not a flat one (as it appears to be). This curvature means that "straight line" is actually not quite what you're used to; things follow straight lines, but those straight lines don't look straight to us, because of the underlying space's curvature: we can't see the whole of spacetime, only small segments of it, so we can't see enough to get a proper sense of the curvature. But since our limited frames of reference have their own notion of "straight line" which is incompatible with that of the global spacetime, we observe a mysterious tendency of things to deviate from what we think is the straight line they should be following. So gravity "is a force": it's a mysterious tendency of things to move, because we are limited in what we can see and our own observation frames are subtly incompatible with the global structure. But it's also "not a force": if we were somehow able to take a fully global view of the universe, there would be no mysterious movement, only a huge number of things moving at exactly the same speed in perfect straight lines through a curved spacetime. (Assuming General Relativity is 100% accurate.)

freshhawk 6y ago

"If you and a friend started walking straight north, both at the equator but a long distance apart, you would gradually get closer to each other until you collided at the north pole." I always thought that was a nice way to drop one dimension down to get the intuition. To the metaphorical 2D ant they see two friends attracted to/falling towards each other, but they are going in a straight line on a curved surface and there are no forces at play.

rokobobo 6y ago

It's been some time since I studied these things, but I believe the post was trying to illustrate that the geodesic lines in spacetime created by Earth's gravity field can be visualized as straight lines after a nonlinear change of the coordinates system. [1] To simplify, these are the lines along which particles move when no outside force is exerted on them--again, considering gravity to be a distortion of spacetime and not a force, very much like the well-known metaphor of steel ball on a rubber sheet, which would curve marbles towards the "well" it's created in the sheet. But you're right that once the marbles and the steel ball get to a point where one of the gravitational fields cannot be ignored, this framework becomes less useful. [1] https://en.wikipedia.org/wiki/Geodesic https://en.wikipedia.org/wiki/Geodesic

dreamcompiler 6y ago

I take your point, but I think the author's main point was that because objects in free-fall merely follow spacetime geodesics, it makes calling gravity a "force" a little bogus, at least compared to the other forces. Tidal effects don't change that; tidal effects mean the spacetime curvature "over here" is different than the spacetime curvature "over there", which means the principle of equivalence isn't true in a global sense. But objects still follow spacetime geodesics, which is a concept that's hard to reconcile with the notion of a "force."

jiggawatts 6y ago
That "perspective" can be extended to other forces. E.g.: one could say that an electron taking a complex spiralling path through a magnetic field on Earth is merely following a "gravity+EM geodesic" and is actually in free fall the whole time.

didibus 6y ago

I'm super layman in all this, but I think the word force here refers to the Newton's force. Which experimentally was shown to not properly predict the effect of gravity, where as seeing gravity as a distortion of spacetime instead of as a acceleration force applied to the objects, did predict accurately the trajectory in experiments. You can call both a force in the generic dictionary definition of force. Because obviously it's crazy that something can be so powerful as to distort spacetime itself. But gravity wouldn't be a force in the Newton sense of being something that affects the acceleration of an object.

Smaug123 6y ago
If you choose to view the universe in one particular coordinate system (e.g. one centred on your eyes), then you'll see some things mysteriously happening. For example, you might find that if you release something from your hand, it will mysteriously move towards your feet. Eventually you'll realise that a bunch of things can cause things to mysteriously move, and you'll start using the word "force" to describe "tendency to mysteriously move". But some of these forces are not observed by other people who are watching; they arise as by-products of the fact that you are the one doing the measuring. For example, if you're falling in a lift, you won't observe the force that causes a ball to fall towards your feet; but I, standing on the ground outside the lift, will observe that actually you and the ball and the lift are subject to this force. In fact there's an underlying reality which we can't directly observe but which we can infer from the paths of objects. That reality is a curved spacetime, not a flat one (as it appears to be). This curvature means that "straight line" is actually not quite what you're used to; things follow straight lines, but those straight lines don't look straight to us, because of the underlying space's curvature: we can't see the whole of spacetime, only small segments of it, so we can't see enough to get a proper sense of the curvature. But since our limited frames of reference have their own notion of "straight line" which is incompatible with that of the global spacetime, we observe a mysterious tendency of things to deviate from what we think is the straight line they should be following. So gravity "is a force": it's a mysterious tendency of things to move, because we are limited in what we can see and our own observation frames are subtly incompatible with the global structure. But it's also "not a force": if we were somehow able to take a fully global view of the universe, there would be no mysterious movement, only a huge number of things moving at exactly the same speed in perfect straight lines through a curved spacetime. (Assuming General Relativity is 100% accurate.)