Proof of the curvature of space-time?

[Roo]

Hey all,

Thought I'd post this here as it is a little tricky trying to get a straight answer from the boys and girls of theory over at the GR/SR section without causing havoc of some kind.

It seems to be fairly well accepted that space-time is curved. So maybe someone here can answer the question of has this been proved without doubt? And I'm talking proved not by maths or theory - but physically and factually. Too many answers to difficult questions are 'solved' by maths to make sure it fits neatly with a given proposal. Personally, with certain things, I don't abide by that rule. I like to know what physical proof there is.

Roo.

 

[Amanheis]

In physics, we don't work with proofs, we work with experiments. There is no way to proof a theory, only a way of verifying it by experiment, that is to make sure it is not wrong. The most direct way of measuring space-time curvature that I can think of of the top of my head is also the first experiment that confirms GR, suggested by Einstein and done by Eddington. Read it up here:
http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington#Relativity
In my opinion one of the most beautiful experiments ever.

Also, GR assumes a curved space, so everything that is predicted by GR relies on the fact that space-time is curved. Look-up the perihelion motion of mercury or the relativistic corrections in GPS satellites.

An even better way to measure the curvature directly would be to measure the sum of inner angles of a sufficiently large triangle. In a curved space, it shouldn't up to 180 degrees. But on large scales, space-time is probably too flat to see any deviations, so this is really hard to accomplish, but physicists are working on that. Gauss tried to it on earth, but he couldn't find any measurable deviations of a flat space.

 

[Chronos]

The jury is out on curvature. All current measures are unable to rule out the flat conjecture.

 

[Roo]

The jury is out? Oh! Why is that? I'm curious...

I'm not saying that I do/don't accept that space-time is curved. It's just that a notion like this sounds a little...well, odd. I'm not a physicist (though I have studied it) nor a mathematician (though, again I have studied it by having an engineering background) and many of my opinions are based on nothing more than practical discrimination.

This has all started because of my interest in FTL propulsion concepts. Of what I have researched, the idea of 'warping' space-time seems to be the current proposal to get around the light barrier problems etc etc. Yet the idea of actually manipulating space-time seems like the most ridiculous notion ever created. How can you physically manipulate a dimension as it were? Ironic, seeming as FTL travel is a major interest to me!

But, I'm not trying to disprove anything, merely ask a few 'practical' based questions. Many theories can be proved by experiments on a small scale, or observations and even by maths. But does it answer it up the ladder on the actual stage as it were? By warping space-time, the idea is to bring two points closer together - but how would that work in actual practice? The question I put on the GR/SR section was that if space-time can indeed be manipulated, then surely how to do it must be known as well, even if the technologically to do such a thing is way, way off in the distant future.

Roo.

 

[George Jones]

The jury is out on curvature.

No, it's not.

All current measures are unable to rule out the flat conjecture.

Phases like "the universe is flat" refer to space, not spacetime. On cosmological scales, measurements indicate that spatial hypersurfaces (orthogonal to cosmic time) of spacetime are flat or almost flat, but spacetime is curved.

It seems to be fairly well accepted that space-time is curved. So maybe someone here can answer the question of has this been proved without doubt?

As Amanheis has already noted, physicsl theories are never proved. Our best theory of gravity, Einstein theory of general relativity, is also a theory of curved spacetime. This theory of gravity as curved spacetime makes physical predictions which physicists try to verify. For a comprehensive account of these predictions and experimental verifications, look at the review article "The Confrontation between General Relativity and Experiment" by Clifford M. Wiil,

http://relativity.livingreviews.org/Articles/lrr-2006-3/ .

Yet the idea of actually manipulating space-time seems like the most ridiculous notion ever created. How can you physically manipulate a dimension as it were?

The central equation of general relativity is called Einstein's equation. One side of Einstein's equation is geometrical and is related to the curvature of spacetime, and the other side is related to the distribution of energy/mass/momentum. Since this is an equation, it is impossible to change just one side: change the geometry side and this means that distribution of energy/mass/momentum must also be changed; change the distribution of energy/mass/momentum, and this means geometry must also be changed.

So, spacetime can be manipulated by moving masses and energy around.

 

[Wallace]

General Relativity is a theory that explains the effects of gravity (i.e. the mass of all things upon the motion of all things) in a geometric way. The geometric nature of the theory leads to the term 'curvature'. As Amanheis suggested, the only way to know if this is the correct theory is to do experiments, and experiments have so far agreed with GR, and hence space-time must curve in the way implied by this theory. That is as much as we can say. It is possible that we could re-formulate GR into a non-geometric theory that was mathematically equivalent and then we wouldn't have 'curvature' of space-time. The notion of curvature is a mathematical construct that gives us the correct answer.

By the sounds of you original post, you've probably been told something like this before but it didn't really satisfy you. Unfortunately your request for an answer 'proved not by maths or theory - but physically and factually' makes no sense. What does it mean for space-time to curve 'physically'? The physical theory, that cannot be separated from the language it is written in (mathematics), describes the effects of gravity as space-time curvature. The theory gives the correct predictions when compared to experiments, and therefore the theory appears correct (at least in the regimes it has been measured in). There is no other way to test a theory more 'factually' than this I'm afraid. Rememeber that space-time is a mathematical construct, so therefore anything is does (such as curve) is also a mathematical construct.

Note that Chronos has misunderstood your question, he is referring to the question of whether when we use a particular solution (the Friedmann-Robertson-Walker model) of GR to describe the large scale Universe, is the spatial part flat or curved. This is a different question, and in either case space-time is curved (even if the spatial part in a particular co-ordinate system is not). If this is confusing then don't worry, but you should realize that the jury is in no way 'out' on the question of space-time curvature explaining gravity, i.e. regarding the bending of light around massive objects. As I say, Chronos is answering a different question, so don't let that confuse you.

On your FLT ideas, note that just because space-time can be curved in GR is not the ticket to a free lunch. Curvature is caused by the presence of mass-energy, so you don't make curvature out of nothing, and you cannot curve space-time in arbitrary ways. The only know sensible description of a warp drive type situation in GR is the http://en.wikipedia.org/wiki/Alcubierre_drive" however it is important to note that this 'solution' to GR requires an energy source that violates many many rules of nature (it have to have a negative energy for starters, which is a non-sensical concept physically). If I was going to write a Sci-Fi story using FLT it would use an Alcubierre drive, but it is still literally impossible based on the current laws of physics. So, as I say, space-time curvature does not mean 'anything goes', the universe still behaves lawfully.

 

[Roo]

Chaps,

Thanks for your answers here, most helpful - and insightful.

Roo.