The Principle Of Relativity With Applications To Physical Science (1922) by Alfred North Whitehead

It is a delight to have this volume back in print again. For anyone with an interest in Whitehead's philosophy, this is an essential work that requires very little discussion. Whitehead is, here and in all of his work, a marvelous writer. But this is a technical piece, not necessarily of interest to the broadest audience imaginable. So, very briefly, what I want to do here is suggest to physicists, physics enthusiasts, and philosophers of science why they need to be interested in this book.

In the physics community, it is well known that Whitehead's theory of relativity is "wrong." Evidence presented by Clifford Will in 1971 articles in the "Astrophysical Journal," which were later summarized in his _Theory and Experiment in Gravitational Physics_ (available at Amazon), "demonstrate" that Whitehead's theory makes predictions that are violations of observational data. Very convincing, and as nearly as I can tell, Will's arguments have only one (or two, depending on how you count) problem(s):

They are predicated on two assumptions, one that is so limited it grossly misconstrues the aims of Whitehead's theory, while the other is demonstrably false.

Will's arguments against Whitehead (which come from the work of J.L. Synge) state up front that Whitehead's theory is based upon a "(1)non-dynamical (2)flat metric." #2 is the limited approach that grossly misconstrues Whitehead's argument, while #1 is the demonstrable falsehood.

It is true that, in the explicit mathematical treatments of the second half of the book, Whitehead is using Euclidean geometry. But the idea that the "flat-metric" plays any central role in Whitehead's theory is explicitly repudiated on the VERY FIRST PAGE of text in Whitehead's book. Whitehead makes it absolutely clear that he is only using "flat" geometry for purposes of mathematical convenience; it plays no essential role in his larger theory. Indeed, in 1923, G. Temple actually generalized Whitehead's program to a non-flat system of mathematics. But, despite the fact that everyone mentions Temple, no one actually looks at his work, or addresses Whitehead's larger arguments in that light.

The claim that Whitehead's theory is "non-dynamical" is demonstrably false. Unfortunately, Whitehead put this demonstration in a book that had been published three-years earlier, his _Enquiry into the Principles of Natural Knowledge_. This, along with _Concept of Nature_ and the finally republished _Principle_ form what might be thought of as the "triptych" of Whitehead's philosophy of nature. All of these books are the results of a common line of inquiry. But, unfortunately (again), Whitehead's argument for the dynamical nature of his theory is only implicit in _The Principle of Relativity_; he assumed people read his other books.

Now, the centerpiece of Whitehead's argument -- the part that Synge explicitly ignores and which Will (following Synge) doesn't even acknowledge -- is the *philosophical* critique of Einstein's theory. This philosophical critique is seldom enough noticed in the philosophical literature; as far as I know, has never been addressed within physics. The criticism is this: if the geometry of space is altered by every last particle of matter and energy which influences space, then there is no possibility of meaningful measurement. In order to measure a piece of space, my unit of measure must have some kind of uniform meaning, such that I can legitimately move my "yardstick" from "here to there." Einsteinian General Relativity undercuts this possibility, by denying the existence of any such uniformity. The structure of space is absolutely dependent upon the contingent distributions of matter and energy.

As a result, before we can engage in meaningful measurements, we must know how matter and energy is distributed throughout the universe so as to know how to interpret our measurements. In other words, if Einstein is right, we're boxed into a situation where the only way we can know anything, we must first know everything.

Clearly, I have the space here for neither a careful nor a detailed examination of Whitehead's argument. There are some interesting responses to this criticism that can be developed from the claim that space exhibits "maximal symmetry" in the abstract. This claim is rarely mentioned even in the orthodox physics literature -- Weinberg and Carroll are the only major texts on the subject which I know that talk about the subject at all. In any case, Whitehead's work is more than deserving of examination, examination that is *NOT* dominated by the narrowest consideration of nothing beyond the mathematical treatments at the end of the book. These, too, are of interest, though by now it would seem more for their historical worth than their direct connection to cutting edge cosmology. Still, even this part is worthy of serious attention, since it is the basis of Whitehead's rejection of the "geometrical metaphors" which so dominate the field.

Published in 1922. There Parts. Part III about tensors is exactly the same subject as paper published by Gregorio Ricci-Curbastro (with his student Tullio Levi-Civita) in Annals of Mathematics in 1901: the greatest life discovery of Ricci: no concept of a vector, because every vector is either contravariant or covariant, and simply `vector' does not exists in algebra, except still in the teaching. Alfred Whitehead never refer to Ricci, presenting covariant and contra variant tensors as this is his personal discovery, probably was not aware the Ricci's publications. Most interesting seems to be is the Part I about philosophy of science, where Whitehead understand correctly the Hermann Minkowski, that position space is a quotient of space-time, and not as it is wrongly presented in present textbooks as the submanifold for each moment. I am happy that I brought this book from Amazon, and recommend to read this for students of mathematics and physics. Title is misleading, there is `The Principle of Relativity' whereas this should be read `The Principle of Gravity'.