# Gravity is curved geometry: A fact of nature or model-dependent interpretation?

We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by matter and energy). However, GR is still only a model, which hasn't been challenged by experimental evidence/precision thus far. E.g., in wiki one might find a lot of alternatives to GR, some of which agree with observations not worse than GR (e.g., Brans-Dicke theory). There are theories which describe gravity not in terms of curvature, but in terms of torsion - but in reality gravity cannot be both at the same time! Besides, as far as I understand, curved space might be described as a curved surface in non-curved space of a higher dimension.

So my question is: do I miss something and there are strong model-independent reasons to believe that gravity is geometry, or is it just that authors in most textbooks and articles imply that this is a model-dependent interpretation, without saying it explicitly?

• What is the difference between "a model consistent with every observation" and a "fact of reality"? What is your epistemological notion of "fact"? – ACuriousMind Dec 6 '14 at 13:15
• I am not a specialist in GR, but I also asked myself this question. So, you can say that gravity is due to the fact that the space is curved. Of course, that invites the question, why is the space curves in some regions and in others it isn't. Then, the answer is there are masses there. But if there are masses, why do we need a curved space, let's talk of gravitational attraction. The mathematics (curved space) is good for handling calculi. (At least, so I answered to myself.) – Sofia Dec 6 '14 at 13:18
• How you interpret the theory is entirely philosophical. The fact is that GR has survived every test thrown at it to date. It also comes with a more 'natural' interpretation than other alternative theories. In addition to that, the curved geometry concept can be applied to other physical theories (e.g Quantum Field Theory in curved spacetime). – Constandinos Damalas Dec 6 '14 at 13:18
• @Sofia: I don't answer the question because I think the premise of the question is meaningless - it supposes that, of two ways of looking at the world, one is "true" and one is "false", even if both predict the same things. There cannot be a difference in truth value between things that predict the same, precisely because our only way to scientifically assess truth (or rather, falsity) is to test predictions. My comment is Popperian rather than Kantian, but it goes in the same direction. – ACuriousMind Dec 6 '14 at 13:31
• Arguably, the existence of space (and time), curved or not, is itself a "model-dependent interpretation", at least as much as its curvature is. – Ilmari Karonen Dec 7 '14 at 16:06