Is it possible to have a mathematically consistent theory of the universe, that describes and explains as much of the scientific observations as does General Relativity, but that does not have warped space?

i.e. it would be a world where space is boringly flat and straight, just as most people imagine it to be, but some other weird things would have to be modified to make it all work out mathematically.

Has any such theory been proposed, or is it pretty much hopeless to try to fit all the experimental data if the model doesn’t allow space (or spacetime) can be warped?

The reason I am asking is that, if it is possible to pose such a theory, even if we end up preferring General Relativity because it makes the math easier, then we can’t really say that spacetime is warped “in reality”, just in the mathematical framework of General Relativity.

On the other hand, if it can be proven that no theory can explain all the existing experimental data without allowing spacetime to warp, then it would be an indicator that spacetime is warped “in reality”, and is not just a mathematical convenience.

Unfortunately, you can’t say that anything exists outside of mathematical convenience. I could say that my desk exists, but I could also say it’s just a mathematical convenience for explaining why my computer doesn’t fall onto the floor. But trying to separate mathematical convenience from reality doesn’t do very much for you, and leaves Ockam with a rather full beard.

Physicist Stephen Weinberg has long argued that the warped spacetime seen in GR is just a mathematical construct with no physical significance, but he’s never really offered any justification for that, and his argument is really no stronger than Copernicus’ argument that the Sun really went around the Earth, but that it was easier on the calculations to assume it was the other way around anyway.

I thought I remembered reading in one of those pop-physics books that a model where spacetime is flat and objects bend towards each other is mathematically equivalent to a model where spacetime warps in the presence of objects. Is there any truth to that?

There have been umpty-gazillion attempts at variations on, alternatives to, and refutations of general relativity ever since Einstein announced it. That’s not news. However, this article does not change the requirement of the OP for non-warped space in any way that I can see. I assume that none of the others do either, except maybe for some that are crackpotly wrong. I don’t remember the one that **Ultrafilter ** maybe is thinking of, though.

With various qualifications, Feynman’s 1962-3 GR lectures (published posthumously as Lectures on Gravitation) played with this sort of idea.

He imagines a hypothetical alien civilisation that has developed quantum field theory, but has never encountered gravity until now. What sort of theory do they come up with to explain it? From the fairly obvious properties of this new phenomenon, they’d deduce that the field quanta have to be spin-2 massless particles (i.e. gravitons). So they start to explore theories involving these. Feynman’s point is to argue that there are fairly natural formal properties that would push them towards a limited set of ways for these gravitons to interact. Ultimately, they’d supposedly come up with the Einstein field equations.
But they wouldn’t know anything about curved spacetime. All of this would be being done assuming that spacetime is flat; massive bodies attract because they are exchanging gravitons. He suggests that eventually some brilliant alien mathematical physicist would belatedly realise that the equations have a geometrical interpretation. So they’d then have two equivalent interpretations of the theory. As originally developed, a theory of matter and gravitons interacting in a flat spacetime. And, in the new interpretation, a theory of matter moving in a dynamic curved spacetime. With no way of experimentally distinguishing between the two.

Of course, historically it was the second interpretation of GR that came first on Earth. Feynman was deliberately presenting the first interpretation as an unconventional way of coming at the subject.
The great difficulty, now as in the 1960s, is that such a simple quantum field theory of gravitons is inconsistent. At the time, Feynman and everyone else could think that that might be easily fixed. That was too optimistic. The whole approach now looks too simplistic and all the subsequent complications tend to mess up the obviousness of the equivalence he was suggesting in the lectures.

Steven Weinberg’s attitude, as mentioned by Chronos, was along much the same lines.

I’m not so sure about that; Feynman several times expressed great suspicion of guage theories, and indeed, that QED, for all of its beautiful, amazingly precise predictions, is a veil which hides the true nature of what’s going on. I recall reading an interview done with him a few years after Murray Gell-Man won his Nobel and Feynman stating that he was suprised that QCD worked out so discretely (as far as it has been worked out).

At any rate, the EFEs work very, very well,at least for as far as we can determine by observation and experiment, and it would be surprising if any subsequent theory is not just an expansion or superset of GR rather than a gestaltic replacement of it.

So what you’re saying here is that the aliens will have a gravitons/curved space duality just the same as we think about particle/wave duality. IOW, two ways of thinking through the problem, but no real change in the mathematics used and no net chang in what is really happening.

You’re muddling together several different issues here. To take it from the end, his surprise about the success of QCD in the 70s doesn’t really say much about his attitude towards quantising gravity in the early 60s. After all, the rough division then had been:

[ul]Hadrons. Strongly coupled. Lots and lots of data, making for piecemeal, but steady, phenomenological progress. Easy for people to contribute and hence where most of the action was. Plenty of proposed approximate theories, but nothing convincingly quantisable. No agreement on what the underlying theory is. People beginning to suggest that the whole area just wasn’t amenable to quantum field theory. Radical suggestions involving ripping all that out and finding some alternative approach, such as Chew’s S-matrix programme. Thus the expectation was that any revolutionary advance would take place in this area.[/ul]
[ul]Gravity. Weakly coupled. Virtually no data. General relativity deeply unfashionable as an area to work in. Not obvious that successfully quantising it would have any profound wider ramifications. But that does provide the obvious classical theory to try to quantise. Quantum gravity could thus be seen as an essentially technical problem. The likes of Feynman could even see a parallel with, very much in hindsight, QED in 1945: the classical theory is a given and it’s just a matter of understanding how to properly quantise it.[/ul]

At the time of the lectures, he could thus be optimistic about reasonably quickly quantising gravity, while pessimistic about sorting out the strong interaction.

On the first point, it’s certainly true that Feynman was generally suspicious about any successful theory being an ultimate answer. But, precisely as a consequence of this, his standards for successfully quantising gravity were rather low. He didn’t think that an accurate quantum theory of gravity was going to immediately yield some Theory of Everything. Indeed he was later to claim in his interviews with Mehra (see The Beat of a Different Drum, sec. 23.1) that his work on gravity in this period had actually pretty much succeeded. Yes, there were still infinities, but their resolution could be relegated to some deeper theory. In other words, he regarded his original optimism as limited but justified.

I don’t think it’s helpful to drag in particle/wave duality here, but otherwise, yes, that’s what Feynman was suggesting.

An excellent discussion of this question can be found in the first couple of chapters of Clifford Will’s book Theory and Experiment in Gravitational Physics, and
also in his online review article “The Confrontation between General Relativity and Experiment.” Basically, we’re led pretty inexorably to the idea that gravity can be described geometrically by the following ideas:
[ol]
[li]The Weak Equivalence Principle holds. This principle basically says that a body’s gravitational mass is always equal to its inertial mass; or in other words, that a body’s trajectory in space, absent non-gravitational forces, is independent of the body’s composition.[/li][li]The principle of “local Lorentz invariance”. This says that (local) experimental results are independent of velocity; for example, if you and I are both orbiting a black hole and our paths cross with some relative velocity v, and we both measure the fine structure constant using some hydrogen atom sitting on our respective ships, we should get the same result.[/li][li]The principle of “local position invariance.” This is basically the same thing as the statement of local Lorentz invariance, only instead of requiring that experimental results be independent of velocity, we require that they be independent of position as well.[/ol]Once you accept these three ideas, then the fact that gravity should admit a geometrical description (i.e. can be described by a curved spacetime) can be shown to follow. Granted, it wouldn’t necessarily need to be described geometrically, as Feynman’s gedankenaliens demonstrate, but the fact that a geometrical description follows so naturally from such basic assumptions makes such a description very compelling to a lot of physicists (myself included.) Of course, it’s possible that tomorrow, we’ll perform some experiment that invalidates one of these three principles, in which case the geometric description of gravity would be in trouble. But there hasn’t been any significant experimental result[sup]1[/sup] that challenges any of these three principles, and not for lack of looking; see section 2.1 of the paper I linked to above for further details.[/li]
Finally, it’s important to note that even once you accept that gravity has a geometrical description, there’s still a huge amount of leeway in how you make the geometry curve in response to a given set of matter. As Exapno Mapcase pointed out, hundreds of alternative gravity theories lie broken & twisted along the road of science, and more are invented every year. However, all of these theories have one thing in common: they postulate a geometrical description of gravity.

[sup]1[/sup] Save one, perhaps: Webb et al.'s quasar study of the fine-structure constant. However, in the six years since it was announced, it hasn’t been reproduced, and I think most physicists are somewhat skeptical of it now.

It’s been a long time since I’ve looked at that paper, but if I recall correctly, even in the original results, the effect was only marginally significant.