Whitehead’s Radically Empirical Theory of General Relativity

“The doctrine of relativity affects every branch of natural science, not excluding the biological sciences. . . . Relativity, in the form of novel formulae relating time and space, first developed in connection with electromagnetism. . . . Einstein then proceeded to show its bearing on the formulae for gravitation. It so happens therefore that owing to the circumstances of its origin a very general doctrine is linked with two special applications.”
–Whitehead (The Principle of Relativity, 3).

One of the biggest surprises for me upon reading Auxier and Herstein’s book The Quantum of Explanation was learning that Whitehead’s theory of extension (or “mereotopology” as it has come to be called) has been taken up by computer scientists working in the field of robotic vision (see for example the work of Ian Pratt-Hartmann).

“It is a widely acknowledged fact in this sub-discipline that Alfred North Whitehead’s work on extension is foundational for their enterprise. Our experience has been that Whitehead scholars are simply astounded to learn of this fact. Yet we should have expected and even predicted such a connection” (QE 90).

Guilty as charged. While I think I got things mostly right in section 3.2 of my dissertation (“From Geometric Conditions of Possibility to Genetic Conditions of Actuality”), the promising application of Whitehead’s topological scheme to robotic vision certainly brings this aspect of his project into sharper focus for me. As a radical empiricist, Whitehead was searching for a formal account of our concrete experience of projectively related extensa. We are finite creatures with limited sensory organs and processing capacity. We do not experience the world of spatial relations in terms of infinitesimal points or the geometrical schemes built up from such points. Rather, what we encounter in our immediate experiential field are the intuitive whole-part relational structures formalized by non-metrical projective geometry.

Following Einstein’s articulation of the special and general theories of relativity (in 1905 and 1916, respectively), and his problematic “mono-metric” identification of a 4-D geometrical model with physical space-time*, Whitehead pursued his theory of extension with renewed urgency. Somehow, the uniformity of spatial geometry had to be preserved, else scientific measurement would become impossible. Einstein did not appear to realize that allowing the contingent warping of space by massive objects undermined the fundamental logical requirements of measurement: that space have a necessary and universal structure (or, as Auxier and Herstein put it, “we must have a standard unit of spatial comparison for conjugacy…and standard(s) of spatial projection” so as to bring this unit into comparison with whatever we are trying to measure [QE 102]). By collapsing the difference between physical space and his favored geometrical scheme, Einstein made the structure of spatial geometry contingent upon randomly arrayed masses.

“We must know the complete distribution of matter and energy in the universe prior to knowing its geometry. But we must have a comprehensive grasp of this geometry in order to discover this distribution. As Whitehead pointed out, with General Relativity as our theory of space and gravity, we are saddled with a situation where we must first know everything before we can know anything” (QE 104).  

Einstein’s “mono-metric” model has been one of the most successful in the history of science. But because of the unexpected observations of the rotational velocity of galaxies and of cosmic inflation rates, its theoretical supremacy has begun to be seriously questioned. Some astrophysicists have attempted to save the theory by inventing “dark matter” and “dark energy” to explain the missing mass that would bring observations back into agreement with Einstein’s theory. Auxier and Herstein refer to these inventions as “an especially unhappy piece of nonsense” (QE 20). I’m sympathetic, but I wouldn’t go quite that far. To my mind, these invented entities are akin to the epicycles of Ptolemaic astronomy. In other words, these exotic and invisible forms of mass/energy (which supposedly compose ~96% of the universe) are postulated ad hoc in an attempt to “save the appearances” (as ancient astronomers used to say). Ancient astronomers were tasked by Plato with explaining the seemingly erratic motion of the planets in terms of a theoretical model composed only of uniform circular motions. When new planetary observations conflicted with the model, more circles were added (epicycles) to bring the model back into alignment with appearances. One view of science is that it is just about refining existing theoretical presuppositions to fit new observations, gradually approaching a perfect identity between model and reality. In this sense, the addition of epicycles to match observations could continue indefinitely. After all, Ptolemy’s geocentric model was more accurate than Copernicus’ heliocentric model (which itself still required epicycles until Kepler and Newton updated his math). The geocentric model is still accurate enough that modern planetarium projectors (invented in the 1920s by a company in Jena, Germany) continue to utilize it, reproducing Ptolemy’s deferents and epicycles with their internal gears and motors (see also).

zeissprojlayout

But as Karl Popper taught us, scientific theories must be subject to empirical falsification. The eternal circular orbits of Ptolemy’s model fall out of phase with the long-term evolution of planetary orbits, while the (updated) heliocentric model accommodates this evolution well. As Thomas Kuhn, another great philosopher of science, taught us, the history of science is not just about the gradual refinement of old theories to fit new observations in an asymptotic convergence of model to reality; rather, this history is also characterized by periods of revolutionary crisis as aging paradigms are supplanted by deeper, wider, more elegant and inclusive explanatory perspectives. Einstein’s genius was to bring the reigning Newtonian theory of gravity into alignment with Maxwell’s theory of electromagnetism. A deeper theory of space was born. But in a sense, despite many other successful observational predictions, empirical falsification is exactly what happened to Einstein’s gravitational theory when it failed to accurately predict the observed rotational velocity of galaxies. However, because this darling model had made a number of other accurate predictions, and because no widely accepted alternative paradigm was on hand, astrophysicists decided to fudge the numbers by inventing new free parameters, new epicycles, to bring the theory back into alignment with observations. Appearances were thereby saved, but at the cost of conjuring into existence an entire universe (or 96% of one, at least) of cold and dark, that is, unobservable, matter/energy.

Even though he did formulate a “bimetric” alternative in 1922 (QE 109), Whitehead’s problem is not with Einstein’s model. This isn’t a “scientists have been wrong before, so why should we trust them now?” argument. Science is about modeling. In some sense, scientific models are always wrong. That’s the name of the game, after all: build a model and throw it against reality until it breaks. Then study why it broke until you find a new model that doesn’t break as quickly. Gradually, more robust, inclusive models emerge. Rather, Whitehead’s problem is with the philosophically naive “model-centrism” that leads scientists to equate their favored model with reality in a dogmatically literalistic way. We should never assume the reigning physical models of the universe offer a final account of the way things are (especially when today’s two most successful models, relativity and quantum theory, remain irreconcilable). Science is not ontology: science is a method of inquiry involving the making and breaking of toy models.

The dogmatic equation of a favored geometrical model with physical reality not only undermined the logical basis of measurement, it led Einstein to dismiss our concrete experience of an irreversible flow of time as nothing more than a “stubbornly persistent illusion.” This is Whitehead’s famous “fallacy of misplaced concreteness” writ large. Einstein’s unquestioned commitment to the classical “spectator theory of knowledge” prevented him from grasping the profoundly relational implications of his new theory of space. He upheld the old Galilean-Cartesian view of a bifurcated Nature, construing our consciousness as somehow external to a cosmos that we can only ever confusedly experience. Whitehead offers an alternative, fully relational epistemology and ontology that re-embeds experience in the cosmos: we are creative participants in a cosmogenetic relational nexus.  

Instead of rushing to eliminate experience from our understanding of a relativistic (or relational) reality, Whitehead carefully examined the hidden epistemic presuppositions and metaphysical requirements of Einstein’s more specific application of relativity to the physics of light and gravitation. The result of his examination was eventually assembled in Process and Reality as the fourth category of explanation, a truly general principle of relativity: “it belongs to the nature of a ‘being’ that it is a potential for every ‘becoming'” (PR 22). Obviously, the importance of Whitehead’s fourth category of explanation (of which there are 26 others) can only be understood within the total gestalt of his categoreal scheme (which includes the category of the ultimate: Creativity; eight categories of existence, among which the most important are eternal objects and actual occasions; and nine categories of obligation). Whitehead’s categoreal scheme is laid out in Part I of Process and Reality as something like an opening credit roll listing the conceptual dramatis personae who, in Part II, will take the stage to exemplify their adequacy. But I’m not going to run through the whole dress rehearsal right now (for a helpful exegesis of Whitehead’s first four categories of explanation, see pgs. 108-110 of QE). Suffice it to say that Whitehead’s principle of relativity expresses the truth that everything co-exists in a web of relatedness, whether actually or potentially. 

Auxier and Herstein:

This is the principle that Einstein and his devotees have abandoned: not the mathematical expression of their physical model; that model is itself only an application of what has become the standard dogma of orthodox cosmology, with its narrowly defined approach to the interpretation of a truncated representation of experience. Rather, physical cosmology has left behind the full principle of relativity and its unqualified commitment to the incurable relatedness of the real. That abandonment comes in the truncation of experience at the root of their largely unexpressed theory of experience [i.e., the theory of the bifurcation of Nature]. For one cannot have a universal principle of relativity—applicable to all that is real—unless one takes experience in its real, relational totality. Experience—both actual and potential—is exactly the kind of reality that falls under the principle of relativity. One cannot take the metaphysical principle of relativity seriously unless one is a radical empiricist” (QE 110). 

In The Quantum of Explanation, Auxier and Herstein have brilliantly succeeded in elucidating the features of a radically empirical cosmology. As Whitehead reminds us early and often in Process and Reality, the purpose of philosophy is not to explain away the existence of the concrete by reduction to the abstract, but to explain the emergence of abstraction from concretion. The proper questions are: how does concrete fact participate in general form and how are general forms exemplified in concrete facts?

For a longer discussion of Whitehead’s radical empiricism a.k.a. relational realism, see my essay “Retrieving Realism: A Whiteheadian Wager.”


*It has been brought to my attention that the matter of whether Einstein thought the physics of gravitation is reducible to the geometry of space-time is not so clear cut. See for example: “Why Einstein did not believe that general relativity geometrizes gravity” by Lehmkuhl. The research continues… 

5 thoughts on “Whitehead’s Radically Empirical Theory of General Relativity

  1. “Following Einstein’s articulation of the special and general theories of relativity (in 1905 and 1916, respectively), and his problematic “mono-metric” identification of a 4-D geometrical model with physical space-time*, Whitehead pursued his theory of extension with renewed urgency. Somehow, the uniformity of spatial geometry had to be preserved, else scientific measurement would become impossible. Einstein did not appear to realize that allowing the contingent warping of space by massive objects undermined the fundamental logical requirements of measurement: that space have a necessary and universal structure (or, as Auxier and Herstein put it, “we must have a standard unit of spatial comparison for conjugacy…and standard(s) of spatial projection” so as to bring this unit into comparison with whatever we are trying to measure [QE 102]).”

    Something analogous appears in the Copenhagen interpretation of QM: Bohr advocated doing away with the law of non-contradiction, which is of course at the foundation of logic and the system of mathematics that are supplying the very evidence he is marshalling to posit this.

  2. What is gravity?
    “Curvature of space-time”

    What curves space-time?
    “The gravitational interia of massive objects”

    What gives the massive objects their gravitational intertia?
    “Curvature of space-time”

    What curves space-time?
    “See above”

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