# What is the proof of gravity being curvature of spacetime?

According to general relativity gravity is an illusion caused by curvature of space-time, rather than real force. As I understand there is overwhelming experimental evidence to support general relativity.

Are there experiments that confirmed specifically gravity as curvature of space-time?

To clarify:

Was there an experiment that shown directly that observable space does not conform to Euclidean geometry? In example (but not limited to): observations of triangles whose angles don't add up to 180 degrees?

• @AccidentalFourierTransform Perhaps i'm misunderstanding "direct" here. Did we actually observe curvature of spacetime? I mean direct observation, ie. triangle with angles that didn't add up to 180 deg. I would assume that something like that would be an direct effect of curved space. – Koder Feb 11 '16 at 22:08
• For this question to make sense, you need to define what "curvature of space-time" is. – Ryan Unger Feb 11 '16 at 22:22
• @0celo7 "deviation of geometry of spacetime from Euclidean geometry" – Koder Feb 11 '16 at 22:34
• Geometry of spacetime? – Ryan Unger Feb 11 '16 at 22:37
• @0celo7 Am I using wrong term? I am no native speaker, perhaps this is an translation error? To elaborate, by "geometry of spacetime" I mean "Geometry of mathematical model that combines space and time". I was under the impression that GR was about defining gravity as gravity as a "geometric property of space and time" and this was correct term to use. – Koder Feb 11 '16 at 22:47

## 1 Answer

If I understand the intent of the question you are asking if we have ever directly measured the deviation of some geometrical object from flat spacetime. For example have we ever measured the internal angles of a triangle and come up with an answer different to $\pi$?

And the answer is yes and no depending on what exactly you mean by measured. For example take a look at the experiment I describe in my answer to What is the sum of the angles of a triangle on Earth orbit?. In principle this experiment could be done, but only at great expense and even then it relies on the the principle that light travels in straight lines.

But if you're prepared to accept the principle that light always travels in straight lines, and therefore that any deviation of the light beam from a straight line is a direct measurement of curvature, then we have directly measured curvature. This is precisely what we measure in gravitational lensing, so the first direct measurement of the curvature was Eddington's measurement in 1919.

If you're not prepared to accept this as a direct measurement then it's hard to see what could possibly count as a direct measurement. How else could you define a straight line to use as a reference for your measurement of the curvature?

• I did some research. By which I mean: i read a lot on internet, I did some thinking, then I read some more. Assumption that light travels in straight lines seems to be key here. If we do, then Eddington's experiment is all we need. If we don't, then what other reference of "straight" we can use? Obviously matter will bend to gravity, we have on-hands example for that. At this point orbit of Mercury hit me - that's the second observation required to assert that "yes, space is non-euclidean" (cutting of other ideas with Ockham's razor). – Koder Feb 13 '16 at 18:08