The full title of this landmark paper is: "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity". The hoax was revealed (simultaneously with the publication) in Alan Sokal's "A Physicist Experiments With Cultural Studies".

In Transgressing, Sokal attacks the view that "can be summarized briefly as follows":

that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in ``eternal'' physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the ``objective'' procedures and epistemological strictures prescribed by the (so-called) scientific method.

Sokal claims, rather, that

It has thus become increasingly apparent that physical ``reality'', no less than social ``reality'', is at bottom a social and linguistic construct; that scientific ``knowledge'', far from being objective, reflects and encodes the dominant ideologies and power relations of the culture that produced it; that the truth claims of science are inherently theory-laden and self-referential; and consequently, that the discourse of the scientific community, for all its undeniable value, cannot assert a privileged epistemological status with respect to counter-hegemonic narratives emanating from dissident or marginalized communities.
Note, in particular, the claim that "physical reality is ... a [social construct]". In later works, Sokal invites anyone who believes this to step out of his apartment window (he lives on the 22nd floor).

So where do these incredible claims come from? Sokal claims to find them in existing post-modernist critique:

These themes can be traced, despite some differences of emphasis, in Aronowitz's analysis of the cultural fabric that produced quantum mechanics; in Ross' discussion of oppositional discourses in post-quantum science; in Irigaray's and Hayles' exegeses of gender encoding in fluid mechanics; and in Harding's comprehensive critique of the gender ideology underlying the natural sciences in general and physics in particular.
In fact, Harding's "difference of emphasis" is huge; the editors of Social Text, despite being experts in Harding (if not in quantum gravity), apparently failed to comment.

The paper's thesis, however, is (if possible) even more startling: that quantum gravity (which physicists have so far been unable to develop) requires such "new thinking" to be developed! Of course, it is hard to imagine any logical argumentation that will lead to this position; it certainly doesn't appear in the paper.

Instead, the mathematically educated reader is treated to a huge variety of nonsense (including the relationship of i in the complex plane to the male phallic organ; this is not Sokal's invention). Any B.Sc. in physics or mathematics should have been able to identify nonsense such as appears in the paper: For example, footnote 60 contains this gem:

For a gentle introduction to set theory, see Bourbaki (1970).
While the Bourbaki books may be a marvel of comprehensiveness and concisesness, nobody learns anything from them.

The list goes on and on. The word "linearity" is (of course) abused; chaos theory relates to nonlinear systems, but this "nonlinearity" has nothing to do with nonlinear thinking. Even strict jargon terms from set theory can be reinterpreted literally, and "valid" conclusions established. Footnote 105 has this:

liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice.
A là Sokal, "choice" here refers to the term used in the U.S.A. in the debate about abortion. Of course, Paul Cohen can be misapplied here, to add to the nonsense:
But this framework is grossly insufficient for a liberatory mathematics, as was proven long ago by Cohen (1966)
What Cohen really showed was that the axiom of choice is independent of ZF; this has nothing to do with, well, almost anything, and certainly nothing to do with any liberal or socialist political agenda.

Especially impressive are the copious footnotes, which contain even more nonsense than the text.

Highly recommended!

In a surprising turn of events, late 2002, the physics establishment seems to have been hit by a hoax similar to that perpetrated by Sokal with his paper Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity, except the other way around.

French brothers, Igor and Grichka Bogdanov, both had their PhD theses accepted by the physics department at Bourgogne university, France, and have published papers in respectable physics journals, such as Annals of Physics and Classical and Quantum Gravity.

Their theory apparently concerns the "topological state" of spacetime, at "scale zero". For example, the abstract from Igor's thesis starts off:

We propose in this research a new solution regarding the existence and the content of the initial spacetime singularity. In the context of topological field theory we consider that the initial singularity of space-time corresponds to a zero size singular gravitational instanton characterized by a Riemannian metric configuration (++++) in dimension D = 4. Connected with some unexpected topological data corresponding to the zero scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in the frame of topological field theory. We get this result from the physical observation that the pre-spacetime is in a thermal equilibrium at the Planck scale.

and concludes:

... we conjecture that the problem of inertial interaction might be explained in terms of topological amplitude connected with the singular zero size gravitational instanton corresponding to the initial singularity of spacetime.

Commenting in the usenet newsgroup sci.physics.research, physics professor John Baez (one of the world's leading mathematical physicists) says he "can [...] assure you that the abstracts seem like gibberish to me, even though I know what most of the buzzwords mean. The journal articles make for rather strange reading [...] Some parts almost seem to make sense, but the more carefully you read them, the less sense they make."

Baez goes on to extract the start of Igor's paper "Topological theory of intertia" (Czechoslovak Journal of Physics, 51 (2001), 1153-1236.) to illustrate his point:

The phenomenon of inertia - or "pseudo-force" according to E. Mach [1] - has recently been presented by J. P. Vigier as one of the "unsolved mysteries of modern physics". Indeed our point of view is that this important question, which is well formulated in the context of Mach's principle, cannot be resolved or even understood in the framework of conventional field theory.

Here we suggest a novel approach, a direct outcome of the topological field theory proposed by Edward Witten in 1988 [3]. According to this approach, beyond the interpretation propoosed by Mach, we consider inertia as a topological field, linked to the topological charge Q = 1 of the "singular zero size gravitational instanton" [4] which, according to [5], can be identified with the initial singularity of space-time in the standard model.

and the conclusion, that

whatever the orientation, the plane of oscillation of Foucault's pendulum is necessarily aligned with the initial singularity marking the origin of physical space S3, that of Euclidean space E4 (described by the family of instants Iβ of whatever radius β), and, finally, that of Lorentzian space-time M4.

According to rumours reported by Baez, the Bogdanovs are "journalists and science fiction writers, both in their late 40's". After gaining fluency in some of the jargon of modern physics by interviewing French string theorists, they "spread rumors that they were geniuses and their theses were a milestone in theoretical physics".

Having made almost a state event of their thesis defences (inviting the national media, wining and dining the president of France, renting a large venue for the occasion) they were both rewarded with passes. Their theses can (at the moment) be found on the "Theses Online" site, at the urls given below.

Information, speculation and rumour, from usenet news article "Physics bitten by reverse Alan Sokal hoax?" <ap7tq6$eme$>, sci.physics.research, 24 October, 2002, by John Baez.

Igor Bogdanov
(Topological state of spacetime at scale zero)

Grichka Bogdanov
(Quantum fluctuations of the signature of the metric at the Planck scale)

Grichka Bogdanov and Igor Bogdanov,
Topological field theory of the initial singularity of spacetime,
Classical and Quantum Gravity 18 (2001), 4341-4372.

Grichka Bogdanov and Igor Bogdanov,
Spacetime Metric and the KMS Condition at the Planck Scale,
Annals of Physics, 295 (2002), 90-97.

Grichka Bogdanov and Igor Bogdanov,
KMS space-time at the Planck scale,
Nuovo Cimento, 117B (2002) 417-424.

Igor Bogdanov,
Topological origin of inertia,
Czechoslovak Journal of Physics, 51 (2001), 1153-1236.

Igor Bogdanov,
KMS state of the spacetime at the Planck scale,
Chinese Journal of Physics. (2002).

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