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This question is asking to better understand the semantics of mainstream physics. My assumption being there is a specific narrative behind the preferred term. In any case, it seems like an essential topic of mainstream physics worth of reflection.

Given we do not know what gravity "is" in any fundamental way, and we are defining its behavior from an external frame of reference, the space-time 'bend' analogy comprises a 'localized' stretch of space as well as a 'localized' dilation of time, but does not seem to semantically account for the gravitational 'pull' itself.

My question respectfully and genuinely asks: why does it seem more appropriate to define the unidirectional gravitational force exerted by any given mass or energy as a mere 'warp', 'bend' or 'curvature' of the space-time fabric instead of a continuous 'pull' of the three-dimensional hypersurface itself. The unidirectional nature of gravity seems more akin to a continuous 'pull' than a bidirectional 'curve'. Conversely, imagine a spaceship moving through a space-time grid at a constant acceleration of 1 g, would you describe it as 'bending' time and space, or 'pulling' through time and space?

Semantically speaking, calling it a 'pull' does not preclude its effect from aligning with a geometric 'curve' (speed per time dilation & direction per space deviation).

I'm not proposing any new theory, nor I believe this question challenges GR in any practical way (time dilation, gravitational lensing, etc). My concern being the semantics getting in the way of a more comprehensive yet intuitive understanding of it.

Lokus Pokus
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    questions questioning the status-quo usually get brush-off and then [closed] It is the explicit policy of this site that only mainstream physics is on-topic. – G. Smith Jul 17 '20 at 16:05
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    @g-smith My question is asking to better understand the semantic of mainstream physics, not to antagonize it or challenge it. – Lokus Pokus Jul 17 '20 at 16:10
  • Comments are not for extended discussion; this conversation has been moved to chat. – tpg2114 Jul 18 '20 at 15:26
  • It's disappointing to see a basic semantic question about the usage of a single word in mainstream physics get [closed] under the pretense of being an 'unpublished personal theory', and to have the scientific answer reduced to 'because it is written'. – Lokus Pokus Jul 20 '20 at 21:19

3 Answers3

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The terminology is used for two reasons.

First, the mathematics used in general relativity for describing gravity is (pseudo) Riemannian geometry. As a result much of the terminology comes from the pre-existing terminology of Riemannian geometry.

Euclidean geometry has a series of axioms which are valid on a flat plane, but which are invalid on a curved surface like a sphere. Riemannian geometry is concerned with the geometrical concepts related to curved surfaces like the surface of a sphere where those axioms do not hold. As a result much of the terminology was developed to reflect the geometrical impact of working in an arbitrarily curved surface. General relativity borrowed the math to describe gravity and the existing terminology came with it.

Second, there are gravitational effects in general relativity that don’t align well with the force concept but do align well with the geometrical concept. For example, gravitational time dilation.

There is no a priori reason that gravitational time dilation would be predicted from a force, and yet it falls out naturally from the geometrical approach and formed one of the earliest experimental triumphs of general relativity. Because the force concept provides no insight to such gravitational effects but the curvature concept does, the terminology makes sense. Furthermore, geometry is highly intuitive, with many insights gained through reasoning about well known curved surfaces.

Finally, it is possible to discuss the force of gravity. The force of gravity is given by the Riemannian formalism as what is known as the Christoffel symbols. In that context the gravitational force has the same status as the centrifugal and Coriolis forces. As such forces make some people uncomfortable or are considered “fictitious” there is a reluctance to adopt that terminology.

Dale
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    Thanks for the insightful answer about the the pre-existing terminology! Anecdotally speaking, gravitational time dilation was one of the things that make me think on the 'pulling' analogy. That is to say, at the verge of an event horizon the gravitational pull of the space fabric is so strong that from the point of view of an outside observer, photons traveling against the pull would seem almost still. – Lokus Pokus Jul 17 '20 at 17:52
  • Since a photon is massless the idea of a force acting on it is problematic anyway, and even if you can make that work it is not a clear connection between that and time dilation. With the geometrical approach the time dilation is natural and inescapable. – Dale Jul 17 '20 at 18:13
  • I understand, but a pull of space fabric itself, is the opposite of a force acting upon a particle. In this case, the photon is moving freely within the flow of the space fabric pull. – Lokus Pokus Jul 17 '20 at 18:20
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    Ah, I got it. That can be done for the Schwarzschild and Kerr spacetimes. It is called the “river model”. It does not generalize to other spacetimes. I did not study it in detail so I am unsure how (or if) the river model explains time dilation. It is not obvious to me that it does, but as I said I didn’t study it in depth. – Dale Jul 17 '20 at 18:33
  • I appreciate your answers and time; and you can now see why I started the question, with the deleted 'editorial'. – Lokus Pokus Jul 20 '20 at 15:35
  • Several of the votes to close were received before I removed the editorial comments, and were (in my view) probably a reaction to those editorial comments which were unnecessary to the question and somewhat provocative. I think if you had not posted them originally the question probably would not have received those early close votes, and then the late close votes would not have reached the threshold. I have voted to reopen, we’ll see what happens. – Dale Jul 20 '20 at 16:29
  • @Lokus There are a couple of posts on the site that talk about the "river model" that Dale mentioned, eg https://physics.stackexchange.com/a/117087/123208 – PM 2Ring Jul 22 '20 at 17:01
  • @pm-2ring Thanks, I read a couple of papers with similar models. As far as you know, are there any intrinsic contradictions between GR and the pulling analogy? I'm trying to understand why this analogy is generally frown upon, particularly when we are already comfortable with an abstract entity that arguably bends and expands. – Lokus Pokus Jul 22 '20 at 18:11
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    @LocusPocus the problem with the model (AFAIK) is that it does not generalize. It works for a Schwarzschild and a Kerr spacetime, but not any others. So it cannot explain much. – Dale Jul 22 '20 at 18:15
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Imagine that you are in a free-falling elevator. You will feel as if you are weightless. There is no way you could tell whether you are falling in a gravitational field, or whether you are in the depths of space, far from any source of gravity. Any experiment you can do will have the same results in both cases.

Actually, there is only one way to detect the presence of gravity -- if you could look out the window and see another elevator falling beside you, you would notice the elevator slowly coming closer to you. This is because both elevators are being drawn toward the center of the earth. In the absence of a gravitational field, any two objects that are "free-falling" (have no forces acting on them) will NOT be drawn closer to each other. In a gravitational field, two objects that are free-falling (have no forces other than gravity acting on them), may be drawn closer together. This is called a tidal effect, and it is gravity's only effect.

This may seem very counter-intuitive. On the surface of the earth, we think that we feel the force of gravity. Actually, though, the force that we feel is the force of the ground preventing us from continuing on our natural, free-falling path.

Now the reason curvature enters into the picture is that the mathematical concept of curvature allows us quantify the effects of a force that is only detectable through its tidal effects. You can imagine two ants crawling in a straight line on a flat surface. If they start out going in the same direction, their paths will never cross. Now imagine they are crawling on a curved surface, like the surface of an apple. Then even if they try their best to go in a straight line, they will find that they are sometimes drawn closer to each other because of the curvature of the apple. The modern view of gravity is that all objects attempt to travel in straight lines, but that gravity bends space. Because of this, objects travelling in "straight" lines may be drawn closer to each other as a result.

Edit You might object to the above reasoning by saying that the falling motion of the elevator is simply offsetting the gravitational effect. That is certainly one way of looking at it. However, since gravity effects all particles (unlike any other force), there is no way to tell whether the elevator is in a gravitational field or not except to look at tidal effects. It is actually conceptually (and mathematically) much simpler to take the view that all particles naturally attempt to move in straight lines, and the curvature caused by gravity can cause them to come together. This approach has led to many useful new predictions that have been experimentally confirmed. Technically, though, you could view gravity as some kind of force if you want. It's just much harder to account for all the new effects when you do it that way.

Edit 2 It can be hard to reconcile this geometrical point of view with everyday experience. As an example, consider two massive balls, at rest with respect to each other in empty space. It can be hard to understand why curvature would cause these two balls to come together, since they are not moving through space. The key thing, however, is that they ARE moving through time. In relativity, space and time are not two separate concepts. Gravity curves both space and time, so as the balls move through time, the gravitational curvature will cause them to bend into each other.

Technically Natural
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  • If an elevator is free-falling at the speed of the gravitational pull, the elevator is effectively offsetting the perception of gravity for anything inside its frame of reference. – Lokus Pokus Jul 17 '20 at 18:16
  • Thanks for the update! Just to clarify, I was not trying to argue that gravity is a force acting upon particles, but a pull acting upon the space fabric itself (river analogy if you like). – Lokus Pokus Jul 17 '20 at 18:51
  • Could it be then, that calling it a 'curvature' better described the static geomatics initially depicted in books and other static media? – Lokus Pokus Jul 17 '20 at 19:46
  • It works just as well in the dynamic case. The only difference is that the curvature changes with time. – Technically Natural Jul 17 '20 at 20:17
  • Got it, I guess I tend to visualize it as the gravitational 'pull' of the fabric changing according a 'curve' representation. – Lokus Pokus Jul 17 '20 at 20:27
  • I added an edit that may clarify how curvature can cause "pulling" – Technically Natural Jul 17 '20 at 21:08
  • I get it, it's just that, for me, thinking in two massive balls pulling the same fabric describes the same two balls coming together in a more natural way and without touching any GR principle. It looks like it's just me though. – Lokus Pokus Jul 17 '20 at 21:24
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I think that the idea of gravity as a curvature of the spacetime leads to the notion that even the $mg$ force we feel comes from it, what is misleading.

For example: all that class of high school problems where it is said to assume $g$ constant and ignore the air resistance are using an approximation of flat spacetime. Because the situation is totally similar to be uniformly accelerated.

That means: half of our idea of what is gravity, either intuitive, either learned in the school is not related to spacetime curvature.

The other half, related to the orbit of planets or satelites requires spacetime curvature. But that difference is normally not mentioned.

Claudio Saspinski
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