system
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human
Is there a non-geometric equivalent to Einstein's theory of general relativity?

If I understand correctly, the geometric approach is what makes this theory so elegant. I wonder if there exists a theory that takes a non-geometric approach and agrees with the general theory of relativity on all (or most) findings at the expense of simplicity.

*EDIT: a bit more clarification after a deleted comment:*

> Define "non-geometric" in specific terms?

*GR abandons the idea of gravity as a force instead treating it as space-time curvature. I suppose related to this is the formulation of the theory with the help of tensor analysis. So my question can be broken down into the following:* 

*(1) is there a way to use some sort of heavily modified Newton's force approach on flat space-time to arrive at the same conclusions, and* 

*(2) is there a way to formulate the theory in terms of something different than tensors (similar to how geometric vectors can be treated purely algebraically by creating a coordinate system).*
gpt
The short answer is yes. In the first half of the 20th century, we came to understand all the non-gravitational forces in terms of *fields*, with the quintessential example being the electric and magnetic forces. In fact, it wasn't just the forces that came to be described this way, but the matter. Field theory came to underlie all of particle physics.

Not long after, people figured out that general relativity could be formulated in much the same way. In this picture, spacetime is flat, and gravity is carried by a *tensor field*. That just means that, much the way that the electromagnetic field is described by a vector, the gravitational field is a matrix. And while it's not a geometrical theory, this particle-physics view of gravity is also very elegant: it turns out that, as long as you demand a few reasonable conditions (like special relativity), the *only* consistent theory for a tensor field which describes gravity is general relativity!

Now this approach agrees with all the findings of GR for a very simple reason - it's the exact same theory, just in a different mathematical language. Instead of looking at things in terms of geometry, you look at fields and particles, just like in the rest of particle physics. Particles, in particular, come in when you introduce quantum mechanics - then each field comes with an associated particle, and the type of field (vector, tensor, etc.) turns out to correspond to how much spin that particle has. In natural units, vector fields have spin 1, tensors have spin 2, and so on. So the statement is that GR is the unique theory of a massless spin-2 field. The associated particle is called a graviton, analogous to the photon in electromagnetism.