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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?

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    $\begingroup$ What is the difference between "a model consistent with every observation" and a "fact of reality"? What is your epistemological notion of "fact"? $\endgroup$ – ACuriousMind Dec 6 '14 at 13:15
  • $\begingroup$ 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.) $\endgroup$ – Sofia Dec 6 '14 at 13:18
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    $\begingroup$ 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). $\endgroup$ – Constandinos Damalas Dec 6 '14 at 13:18
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    $\begingroup$ @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. $\endgroup$ – ACuriousMind Dec 6 '14 at 13:31
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    $\begingroup$ Arguably, the existence of space (and time), curved or not, is itself a "model-dependent interpretation", at least as much as its curvature is. $\endgroup$ – Ilmari Karonen Dec 7 '14 at 16:06
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The interpretation of gravity as curvature of spacetime is model-dependent. You already mentioned the teleparallel equivalent of general relativity, modelling gravity by torsion. Another possibility are bi-metric theories, where the metric is a more ordinary field on a fixed background (this should be more in line with how string theorists tend to think of gravity - it's just another field, but somewhat special because it has spin 2).

However, GR does have a few things going for it: For example, in principle, we could violate the equivalence principle in teleparallel gravity. So if we're going that way, the equivalence principle becomes a new assumption, whereas in GR, it follows naturally from the geometry. Similarly, if a bi-metric theory is equivalent to GR, the background metric needs to be un-observable, and that's something of a 'design-smell'.

GR is the most aesthetically pleasing description of gravity I'm aware of - which has no relevancy to how the universe 'really' works. That's not a question physics can answer - science is not in the business of 'everlasting truth'.

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    $\begingroup$ Nice last paragraph and exactly in line with what I had in mind. +1 $\endgroup$ – Constandinos Damalas Dec 6 '14 at 13:27
  • $\begingroup$ @ Cristoph : not everybody studied GR is depth. I looked in Wikipedia to see what is teleparallelism. But, isn't this a queer idea (with all the due respect to Einstein)? The gravitational forces are of extremely long range, the electrostatic forces are of incomparable shorter range. $\endgroup$ – Sofia Dec 6 '14 at 13:52
  • $\begingroup$ @Sofia: is unifying gravity and electromagnetism really more unreasonable than electroweak unification? anyway, I was talking about the teleparallel equivalent of GR, which does not include electromagnetism; see the preprint (PDF) of this book for details on teleparallel gravity and this article for a different perspective $\endgroup$ – Christoph Dec 6 '14 at 14:05
  • $\begingroup$ I like it how your answer also answered various questions about gravity from string theory ("Another possibility are bi-metric theories, where the metric is a more ordinary field on a fixed background (this should be more in line with how string theorists tend to think of gravity - it's just another field, but somewhat special because it has spin 2).") way better (more pedagogically) than the actual answers to those questions. +1 $\endgroup$ – Danijel Dec 6 '14 at 21:52
  • $\begingroup$ I don't understand how are they equivalent if they require the underlying spacetime manifold to be something very restictive. For example if it is supposed to be Minkowski or parallelizable how can the theory be equivalent to GR! $\endgroup$ – MBN Dec 7 '14 at 13:05

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