# Is there proof gravity bends space or is it just the most convenient explanation?

I have read this sentence in an article:

The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a force, said Einstein, but because space and time around the object are curved.

Do we have a physical evidence that this is in fact true? By evidence I mean stronger explanation than just Occam's Razor, that dictates that bent curvature of space is more plausible/shorter/elegant explanation than let's say gravitational pull being mediated by graviton particle?

EDIT: I understand now that my question does not make the sense I thought it did. Gravity explained by a force between two objects manifests differently than gravity explained by curvature of space and we have measured the difference. Maybe the first part of my question may be of some interest - whether there are other indication of curved space - but I understand now it is the ONLY valid metaphor we have.

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You can't prove anything in physics. We observe, test, and propose axioms (aka laws) which fit known data and correctly predict future events. To that extent, GR is a valid measure of the universe. – Carl Witthoft Nov 18 at 13:44
Didn't Einstein also state that mass created space-time? I don't think that is well-regarded at this point. – Jiminion Nov 18 at 19:08

There is no %100 proof in science; at least not for good science. It's always a question of being the most accurate / descriptive / useful theory. For example, Newtonian gravity is 'true' to the extent that it is very effective in a huge diversity of situations. General Relativity (GR) includes all of the accuracies of Newtonian Gravity, and then also explains a huge variety of additional phenomenon where Newtonian Gravity fails. We think that there are places where GR is incomplete: when you need to also describe things on the quantum mechanical scales. There are also some quirks about the 'dark sector' (Dark Matter, and Dark Energy) that we don't really understand. But, for all intents-and-purposes, GR can satisfactorily explain all observed gravitational phenomenon, including a wide variety of 'Tests of GR' --- which, very importantly, no other theory is able to do.

At the same time, the description of gravity through General Relativity is intrinsically that of 'curved' spacetime. The 'metric' of GR is fundamentally, and inextricably, a description of the very geometry of 3+1 spacetime which, purely from that, describes all of the resulting gravitational dynamics. A GR description is effectively synonymous with a curved-space-time description. To my knowledge, this is also unique to GR. Thus, by demonstrating the accuracy of GR, the validity of viewing gravity as curved spacetime is demonstrated. As described in this first paragraph, this should still subject to the same interpretation that this is currently the best description of observable properties of the universe.

## Tests of General Relativity (brief summary, see wikipedia for details)

• "Perihelion Precession of Mercury" (dynamics) : Mercury's orbit is not perfectly closed ellipses, but instead 'precesses' (rotates slightly). The exotic dynamical effects have also been observed by space missions, and in the dynamics of stars moving near the massive black-hole in our galactic center.
• "Deflection of light by the sun" (lensing) : the path of light is observed to be deflected by massive objects. This was observed in the light of single stars moving behind the sun, but has since been extended to examples of completely distorted or duplicated images of galaxies, or subtle statistical effects to large fields of distant galaxies. The cause of the deflection (as read by GR) is very literally curvature of spacetime --- causing all objects (even photons, without rest-mass) to be deflected.
• "Gravitational Redshift" (light travel) : The frequency of light is 'redshifted' as it changes it's depth in gravitational potential wells. Similarly, the delaying effects of warped spacetime have long been observed, and is a very important component of how GPS works.
• Binary Pulsar (Gravitational Waves) : The orbital decay of the 'Hulse-Taylor' Binary-Pulsar is consistent with the emission of gravitational waves to an incredible precision, and won a Nobel prize. Gravitational waves are, very literally, traveling ripples in space-time which are able to carry energy.
• Cosmology : The expansion of space, and especially inflation, fit very nicely and naturally into the GR context --- because it describes the space-time itself, explicitly, instead of only the objects inside of it. The only alternative explanations we have for these observations are extremely convoluted - and require many different tools for different regimes (i.e. changing mass/light-speed etc may kind-of explain expansion observations, but you need something else to explain homogeneity and yet another thing for the horizon or monopole problem, etc). This is another example of a dynamic, flexible spacetime being employed.

In the very near future we expect to directly detect gravitational waves using Pulsar Timing Arrays and ground-based Laser Interferometers. This would be a 'nail in the coffin' for interpretation of gravity as spacetime.

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Nobody is denying that General Relativity has been experimentally confirmed many times. Your answer does not explain how is the concept of curvature of space more accurate / descriptive / useful theory than let's say the concept of gravitation force or field filed. – daniel.sedlacek Nov 19 at 14:53
@daniel.sedlacek, I'm sorry I was off-focus. I've tried to update my answer. The crux is that GR is effectively synonymous with space-time curvature. Let me know if there's still anything unclear. – DilithiumMatrix Nov 19 at 15:14
I agree with daniel - the issue was not whether GR is accurate, but has to do with interpretation. Interpretations are important, because they guide the mind when innovating and finding new ideas, among others. From a GPS engineer's point of view, it's of course irrelevant, but from a researcher's PoV it might be instructive to try to see things in other ways sometimes. Having said that, I think the current graviton models are for conceptually modelling quantum gravity in the weak field limit. – BjornW Nov 19 at 15:58
@BjornW, please let me know how I can better address that issue. – DilithiumMatrix Nov 19 at 16:00
I'm not sure, as there is no real quantized theory of gravity (so far :). I guess it's the premise of the question which was a bit optimistic. I noted that the OP added an edit to the question as well about this. – BjornW Nov 20 at 17:02

I found the Weinberg passage, but to quote it I need to do it in an answer (too long). So here it goes.

We have seen in this chapter that the nonvanishing of the tensor $R_{\lambda \mu \nu \kappa}$ is the true expression of the presence of a gravitational field. We also saw in Chapter 1 that Gauss was led to introduce the Gaussian curvature $K = -R/2$ as the true measure of the departure of a two-dimensional geometry from that of Euclid, and that Riemann subsequently introduced the curvature tensor $R_{\lambda \mu \nu \kappa}$ to generalize the concept of curvature to three or more dimensions. It is therefore not surprising that Einstein and his successors have regarded the effects of a gravitational field as producing a change in the geometry of space and time. At one time it was even hoped that the rest of physics could be brought into a geometric formulation, but this hope has met with disappointment, and the geometric interpretation of the theory of gravitation has dwindled to a mere analogy, which lingers in our language in terms like "metric," "affine connection," and "curvature," but is not otherwise very useful. The important thing is to be able to make predictions about images on the astronomers' photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effect of gravitational fields on the motion of planets and photons or to a curvature of space and time. (The reader should be warned that these views are heterodox and would meet with objections from many general relativists.)

I could complement what Weinberg said, but... Well, I don't see why. I think it's pretty clear and awesome.

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That was Weinberg's view in the 70s, but I think he has since changed his mind. And as Weinberg himself notes, this is a minority opinion. Probably more so today than when Weinberg wrote his book. If you had quoted from the contemporaneous Misner, Thorne, and Wheeler instead the view would have been very, very different. That book emphasizes geometric thinking throughout. – Robin Ekman Nov 18 at 16:56
Yes, I agree. I just think that Weinberg's view, as he himself said, is heterodox and very interesting. It might have changed over the years, but I don't see why the non-geometrical point of view can't be taken into account. As the quote says, "it simply doesn't matter whether we ascribe these predictions to the physical effect of gravitational fields on the motion of planets and photons or to a curvature of space and time", so I thought this point of view deserved to be mentioned. – QuantumBrick Nov 18 at 17:05
I suppose this is the GR version of "shut up and calculate". – Benito Ciaro Nov 20 at 6:03

There's a very real phenomenon called 'Gravitational Lensing', in which light is bent from its original trajectory by a massive enough cluster of matter (which curves the space-time around it). Moreover, it's bent by a different amount than predicted by a simply application of Newtonian ideas, as kindly pointed out by Rob Jeffries. Is this evidence enough? =]

https://en.wikipedia.org/wiki/Gravitational_lens

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You might add - and bent by a different amount than predicted by a simply application of Newtonian ideas. – Rob Jeffries Nov 19 at 15:30