In the September “Einstein” issue of Scientific American, readers are granted the impression that gravity is caused by curvature of space-time. As an example, on the 1st page of that section, we read “gravity … is the by-product of a curving universe”, on p. 43 we find that “the Einstein tensor G describes how the geometry of space-time is warped and curved by massive objects”, and on p. 56 there is a reference to “Albert Einstein’s explanation of how gravity emerges from the bending of space and time”.
In reality, lots of physicist today emphasize “curvature” as the definition for gravity. As Stephen Hawking penned in A Brief History of Time, “Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or warped.”.
The issue is, that’s NOT what Einstein said. Einstein made it quite clear that gravity is a force just like other forces, along with (of course) specific distinctions. In the actual paper cited by Scientific American (“The foundation of the general theory of relativity”, 1916) he wrote,” [there is] a field of force, namely the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies”. The G tensor, said Einstein “describes the gravitational field.” The term “gravitational field” or just “field” occurs 58 times in this article, while the term “curvature” does not appear whatsoever (besides in relation to “curvature of a ray of light”). And Einstein is not the only physicist who thinks that. For instance Sean Carroll, a prominent physicist of today, wrote:.
Einstein’s general relativity describes gravity in terms of a field that is defined at every point in space … The world is really made out of fields … deep down it’s really fields … The fields themselves aren’t “made of” anything– fields are what the world is made of … Einstein’s … “metric tensor”… can be thought of as a collection of ten independent numbers at every point.– Sean Carroll.
To suppress the field concept and emphasize “curvature” not only misstates Einstein’s view; it also gives individuals an incorrect or misleading understanding of general relativity.
So where does “curvature” come from? According to Einstein (in the cited paper), the gravitational field causes physical adjustments in the length of measuring rods (just like temperature can cause such changes) and it is these changes that produce a non-Euclidean metric of space. In fact, as Einstein pointed out, these changes can take place even in a space which is devoid of gravitational fields– i.e., a rotating system. He then proved that this non-Euclidean geometry is mathematically equal to the geometry on a curved surface, which had been developed by Gauss and extended (mathematically) to any amount of dimensions by Riemann. That this is a mathematical equivalence is distinctly stated by Einstein in a later paper: “mathematicians long ago solved the formal problems to which we are led by the general postulate of relativity”.
For my complete article on the disparity of Einstein’s theory of relativity visit the blog at Fields of Color.