## 28 Oct Scientific American, EINSTEIN DIDN’T SAY THAT!

In the September “Einstein” issue of Scientific American, readers are given the impression that gravity is caused by curvature of space-time. For example, on the first 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 fact, many physicist today emphasize “curvature” as the explanation for gravity. As Stephen Hawking wrote 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 problem is, that’s NOT what Einstein said. Einstein made it quite clear that gravity is a force like other forces, with (of course) certain differences. In the very 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 word “curvature” doesn’t appear at all (except in regard to “curvature of a ray of light”). And Einstein is not the only physicist who believes that. For example Sean Carroll, a leading 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 focus on “curvature” not only misstates Einstein’s view; it also gives people a false or misleading understanding of general relativity.

So where does “curvature” come from? According to Einstein (in the cited paper), the gravitational field causes *physical changes* in the length of measuring rods (just as temperature can cause such changes) and it is these changes that create a *non-Euclidean metric* of space. In fact, as Einstein pointed out, these changes can occur even in a space which is free of gravitational fields – i.e., a rotating system. He then showed that this non-Euclidean geometry is mathematically equivalent to the geometry on a curved surface, which had been developed by Gauss and extended (mathematically) to any number of dimensions by Riemann. That this is a mathematical equivalence is clearly 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**”.

Well, you may say, if the gravitational field is equivalent to curvature of space-time, what difference does it make? It makes a lot of difference.

First, most people cannot visualize physically four-dimensional curvature, while the fact is, they don’t have to. The curvature of space-time, although mathematically equivalent, is not necessary for a complete understanding of Einstein’s theory. The field concept, introduced by Faraday in 1845, is all that is needed.

Second, by eliminating or suppressing the role of the gravitational field, you destroy the great unity that the field concept brings to physics. To quote Nobel laureate Frank Wilczek:

**Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view… the field view makes Einstein’s theory of gravity look more like the other successful theories of fundamental physics, and so makes it easier to work toward a fully integrated, unified description of all the laws. As you can probably tell, I’m a field man.**

Finally, the theory that many physicists believe is our best and most consistent description of reality, Quantum Field theory, has once again been ignored. For example, calling the uncertainty principle an unresolved mystery that “not even the great Einstein” could solve (p. 48), ignores the fact that in QFT it is a natural consequence of the way fields behave. And to say (p. 34): “Relativity and quantum mechanics are just as incompatible as they ever were”, ignores the fact that they are united in Quantum Field Theory. In August 2013 Scientific American printed an article that actually dismissed Quantum Field Theory as invalid because the fields described by the theory are not “what physicists classically understand by the term field”. (To which one can only reply, “Duh, maybe that’s why they’re called quantum fields.”)

Please note that it is not just me who believes that the field concept is central to the understanding of general relativity. That is also the view of, among others, Sean Carroll and Nobel laureates Julian Schwinger, Frank Wilczek, and Steven Weinberg.

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