Read an Excerpt
Chapter One
ALAN SOKAL
Transgressing the Boundaries: Toward a Transformative
Hermeneutics of Quantum Gravity
Social Text, Spring-Summer 1996
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Transgressing disciplinary boundaries ... [is] a subversive undertaking since it is likelyto violate the sanctuaries of accepted ways of perceiving. Among the most fortifiedboundaries have been those between the natural sciences and the humanities.—ValerieGreenberg, Transgressive Readings
The struggle for the transformation of ideology into critical science ... proceeds on thefoundation that the critique of all presuppositions of science and ideology must be theonly absolute principle of science.—Stanley Aronowitz, Science as Power
There are many natural scientists, and especially physicists, who continue toreject the notion that the disciplines concerned with social and cultural criticismcan have anything to contribute, except perhaps peripherally, to theirresearch. Still less are they receptive to the idea that the very foundations oftheir worldview must be revised or rebuilt in the light of such criticism.Rather, they cling to the dogma imposed by the long post-Enlightenmenthegemony over the Western intellectual outlook, which can be summarizedbriefly as follows: that there exists an external world, whose properties areindependent of any individual human being and indeed of humanity as awhole; that these properties are encoded in "eternal" physicallaws; and thathuman beings can obtain reliable, albeit imperfect and tentative, knowledgeof these laws by hewing to the "objective" procedures and epistemologicalstrictures prescribed by the (so-called) scientific method.
But deep conceptual shifts within twentieth-century science have underminedthis Cartesian-Newtonian metaphysics (Heisenberg 1958; Bohr 1963);revisionist studies in the history and philosophy of science have cast furtherdoubt on its credibility (Kuhn 1970; Feyerabend 1975; Latour 1987; Aronowitz1988b; Bloor 1991); and, most recently, feminist and poststructuralistcritiques have demystified the substantive content of mainstream Westernscientific practice, revealing the ideology of domination concealed behindthe facade of "objectivity" (Merchant 1980; Keller 1985; Harding 1986, 1991;Haraway 1989, 1991; Best 1991). It has thus become increasingly apparent thatphysical "reality" no less than social "reality" is at bottom a social andlinguistic construct; that scientific "knowledge;' far from being objective,reflects and encodes the dominant ideologies and power relations of theculture that produced it; that the truth claims of science are inherentlytheory-laden and self-referential; and consequently, that the discourse of thescientific community, for all its undeniable value, cannot assert a privilegedepistemological status with respect to counterhegemonic narratives emanatingfrom dissident or marginalized communities. These themes can betraced, despite some differences of emphasis, in Aronowitz's analysis of thecultural fabric that produced quantum mechanics (1988b, esp. chaps. 9 and12); in Ross's discussion of oppositional discourses in post-quantum science(1991, intro, and chap. 1); in Irigaray's and Hayles's exegeses of gender encodingin fluid mechanics (Irigaray 1985; Hayles 1992); and in Harding's comprehensivecritique of the gender ideology underlying the natural sciences ingeneral and physics in particular (1986, esp. chaps, 2 and 10; 1991, esp.chap. 4).
Here my aim is to carry these deep analyses one step further, by takingaccount of recent developments in quantum gravity: the emerging branch ofphysics in which Heisenberg's quantum mechanics and Einstein's generalrelativity are at once synthesized and superseded. In quantum gravity, as weshall see, the space-time manifold ceases to exist as an objective physical reality;geometry becomes relational and contextual; and the foundational conceptualcategories of prior science—among them, existence itself—becomeproblematized and relativized. This conceptual revolution, I will argue, hasprofound implications for the content of a future postmodern and liberatoryscience.
My approach will be as follows. First, I will review very briefly some of thephilosophical and ideological issues raised by quantum mechanics and byclassical general relativity. Next, I will sketch the outlines of the emergingtheory of quantum gravity and discuss some of the conceptual issues itraises. Finally, I will comment on the cultural and political implications ofthese scientific developments. It should be emphasized that this essay is ofnecessity tentative and preliminary; I do not pretend to answer all the questionsthat I raise. My aim is, rather, to draw the attention of readers to theseimportant developments in physical science and to sketch as best I can theirphilosophical and political implications. I have endeavored here to keepmathematics to a bare minimum; but I have taken care to provide referenceswhere interested readers can find all requisite details.
[1] Quantum Mechanics: Uncertainty, Complementarity,
Discontinuity, and Interconnectedness
It is not my intention to enter here into the extensive debate on the conceptualfoundations of quantum mechanics. Suffice it to say that anyone whohas seriously studied the equations of quantum mechanics will assent toHeisenberg's measured (pardon the pun) summary of his celebrated uncertaintyprinciple:
We can no longer speak of the behaviour of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively ...
When we speak of the picture of nature in the exact science of our age, we do not mean a picture of nature so much as a picture of our relationships with nature.... Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man [sic] and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation. In other words, method and object can no longer be separated. (Heisenberg 1958, 28-29; emphasis in original)
Along the same lines, Niels Bohr (1928; cited in Pais 1991, 314) wrote: "An independentreality in the ordinary physical sense can ... neither be ascribed tothe phenomena nor to the agencies of observation." Stanley Aronowitz (1988b,251-56) has convincingly traced this worldview to the crisis of liberal hegemonyin Central Europe in the years prior and subsequent to World War I.
A second important aspect of quantum mechanics is its principle of complementarity,or dialecticism. Is light a particle or a wave? Complementarity"is the realization that particle and wave behavior are mutually exclusive, yetthat both are necessary for a complete description of all phenomena" (Pais1991, 23). More generally, notes Heisenberg,
the different intuitive pictures which we use to describe atomic systems, although fully adequate for given experiments, are nevertheless mutually exclusive. Thus, for instance, the Bohr atom can be described as a small-scale planetary system, having a central atomic nucleus about which the external electrons revolve. For other experiments, however, it might be more convenient to imagine that the atomic nucleus is surrounded by a system of stationary waves whose frequency is characteristic of the radiation emanating from the atom. Finally, we can consider the atom chemically.... Each picture is legitimate when used in the right place, but the different pictures are contradictory and therefore we call them mutually complementary. (1958, 40-41)
And once again Bohr (1934; cited in Jammer 1974, l02): "A completeelucidation of one and the same object may require diverse points of viewwhich defy a unique description. Indeed, strictly speaking, the consciousanalysis of any concept stands in a relation of exclusion to its immediateapplication." This foreshadowing of postmodernist epistemology is by nomeans coincidental. The profound connections between complementarityand deconstruction have recently been elucidated by Froula (1985) and Honner(1994), and, in great depth, by Plotnitsky (1994).
A third aspect of quantum physics is discontinuity, or rupture: as Bohr(1928; cited in Jammer 1974, 90) explained, "[the] essence [of the quantumtheory] may be expressed in the so-called quantum postulate, which attributesto any atomic process an essential discontinuity, or rather individuality,completely foreign to the classical theories and symbolized by Planck'squantum of action" A half century later, the expression "quantum leap" hasso entered our everyday vocabulary that we are likely to use it without anyconsciousness of its origins in physical theory.
Finally, Bell's theorem and its recent generalizations show that an act ofobservation here and now can affect not only the object being observed—asHeisenberg told us—but also an object arbitrarily far away (say, on Andromedagalaxy). This phenomenon—which Einstein termed "spooky"—imposesa radical reevaluation of the traditional mechanistic concepts ofspace, object, and causality, and suggests an alternative worldview in whichthe universe is characterized by interconnectedness and (w)holism: whatphysicist David Bohm (1980) has called "implicate order." New Age interpretationsof these insights from quantum physics have often gone overboardin unwarranted speculation, but the general soundness of the argumentis undeniable. In Bohr's words, "Planck's discovery of the elementaryquantum of action ... revealed a feature of wholeness inherent in atomicphysics, going far beyond the ancient idea of the limited divisibility ofmatter" (Bohr 1963, 2; emphasis in original).
[2] Hermeneutics of Classical General Relativity
In the Newtonian mechanistic worldview, space and time are distinct andabsolute. In Einstein's special theory of relativity (1905), the distinction betweenspace and time dissolves: there is only a new unity, four-dimensionalspace-time, and the observer's perception of "space" and "time" dependson her state of motion. In Hermann Minkowski's famous words (1908):"Henceforth space by itself, and time by itself, are doomed to fade away intomere shadows, and only a kind of union of the two will preserve an independentreality" (translated in Lorentz et al. 1952, 75). Nevertheless, the underlyinggeometry of Minkowskian space-time remains absolute.
It is in Einstein's general theory of relativity (1915) that the radical conceptualbreak occurs: the space-time geometry becomes contingent and dynamical,encoding in itself the gravitational field. Mathematically, Einsteinbreaks with the tradition dating back to Euclid (which is inflicted on high-schoolstudents even today!), and employs instead the non-Euclidean geometrydeveloped by Riemann. Einstein's equations are highly nonlinear, whichis why traditionally trained mathematicians find them so difficult to solve.Newton's gravitational theory corresponds to the crude (and conceptuallymisleading) truncation of Einstein's equations in which the non-linearityis simply ignored. Einstein's general relativity therefore subsumes all theputative successes of Newton's theory, while going beyond Newton to predictradically new phenomena that arise directly from the nonlinearity: thebending of starlight by the sun, the precession of the perihelion of Mercury,and the gravitational collapse of stars into black holes.
General relativity is so weird that some of its consequences—deduced byimpeccable mathematics, and increasingly confirmed by astrophysical observation—readlike science fiction. Black holes are by now well known, andwormholes are beginning to make the charts. Perhaps less familiar is Gödel'sconstruction of an Einstein space-time admitting closed timelike curves:that is, a universe in which it is possible to travel into one's own past!
Thus, general relativity forces upon us radically new and counterintuitivenotions of space, time, and causality; so it is not surprising that it has had aprofound impact not only on the natural sciences but also on philosophy,literary criticism, and the human sciences. For example, in a celebratedsymposium three decades ago on Les Langages critiques et les sciences del'homme, Jean Hyppolite raised an incisive question about Jacques Derrida'stheory of structure and sign in scientific discourse:
When I take, for example, the structure of certain algebraic constructions [ensembles], where is the center? Is the center the knowledge of general rules which, after a fashion, allow us to understand the interplay of the elements? Or is the center certain elements which enjoy a particular privilege within the ensemble? ... With Einstein, for example, we see the end of a kind of privilege of empiric evidence. And in that connection we see a constant appear, a constant which is a combination of space-time, which does not belong to any of the experimenters who live the experience, but which, in a way, dominates the whole construct; and this notion of the constant—is this the center?
Derrida's perceptive reply went to the heart of classical general relativity:
The Einsteinian constant is not a constant, is not a center. It is the very concept of variability—it is, finally, the concept of the game. In other words, it is not the concept of something—of a center starting from which an observer could master the field—but the very concept of the game.
In mathematical terms, Derrida's observation relates to the invariance ofthe Einstein field equation Gµv = 87[Pi]GTµv under nonlinear space-time diffeomorphisms(self-mappings of the space-time manifold that are infinitelydifferentiable but not necessarily analytic). The key point is that this invariancegroup "acts transitively": this means that any space-time point, if itexists at all, can be transformed into any other. In this way the infinite-dimensionalinvariance group erodes the distinction between observer andobserved; the [Pi] of Euclid and the G of Newton, formerly thought to beconstant and universal, are now perceived in their ineluctable historicity;and the putative observer becomes fatally de-centered, disconnected fromany epistemic link to a space-time point that can no longer be defined bygeometry alone.
[3] Quantum Gravity: String, Weave, or Morphogenetic Field?
However, this interpretation, while adequate within classical general relativity,becomes incomplete within the emerging postmodern view of quantumgravity. When even the gravitational field—geometry incarnate—becomes anoncommuting (and hence nonlinear) operator, how can the classical interpretationof Gµv as a geometric entity be sustained? Now not only the observer,but the very concept of geometry, becomes relational and contextual.
The synthesis of quantum theory and general relativity is thus the centralunsolved problem of theoretical physics; no one today can predict withconfidence what will be the language and ontology, much less the content, ofthis synthesis, when and if it comes. It is, nevertheless, useful to examinehistorically the metaphors and imagery that theoretical physicists have employedin their attempts to understand quantum gravity.
(Continues...)
Excerpted from The Sokal Hoax by . Copyright © 2000 by University of Nebraska Press. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
