“Deconstruction” is a method of critical analysis of philosophical and literary language that emphasizes the internal workings of language and conceptual systems, the relational quality of meaning, and the assumptions implicit in forms of expression.
Todays most fascinating paper is without doubt the one by Bert Schroer entitled:
String theory deconstructed (a detailed critique of the content of ST from an advanced QFT viewpoint)
In this paper Bert (BS) supposedly gives “a detailed and comprehensive critique of claims and methods of string theory from an advanced quantum field theoretical viewpoint.” BS starts out by listing nine claims of string theory “which afterwards will be shown to be fundamentally flawed”. These nine claims are:
1 ) The Kaluza-Klein argument can be used in QFT (or ST) to encode compactified spatial coordinates into inner symmetries
2 ) In ST supersymmetry is spontaneously broken
3 ) Holography is a construct which needs quantum gravity as a prerequisite
4 ) The Maldacena conjecture is about a AdS—CFT holography
5 ) The counting zero mode degree of freedom estimate about the cosmological
constant is consistent with the principle of local covariance
6 ) String theory solves the “information paradox”
7 ) Strings are quantum objects with a localization in spacetime which is
string- instead of point-like
8 ) It has been shown that ST contains QFT in the limit of low energies.
9) The S-matrix of ST has the properties of a particle physics S-matrix
For one thing, BS does not like KK compactifications (claim #1), since “I recently red that already Pauli had shown that this is impossible, but there was no reference given.” And concerning claim 3), BS states that “I think that anybody who knows the framework of particle physics (say beyond the level of recent QFT texts which where written by string theorists) would agree that holography from d+1 to d dimension and its possible inversion cannot be anything else than a radical change of the spatial encoding of a specified algebraic substrate; using this word for anything else would be a misuse and lead to misunderstandings.” This seems to debunk the idea that holography should be related to quantum gravity.
But BS’s arguments against “the Maldacena conjecture” are even stronger. For example, he says that “I do not know any competent quantum field theorist who does not accept Rehren’s work as the correct formulation of AdS—CFT holography (Hollands, Wald, Brunetti, Fredenhagen, Verch, Buchholz, …)”. It is – at least to me – unclear what the …’s stand for here; but even more staggering are BS’s adventures into advanced psychoanalysis: “For psychologically understandable reasons it was this metaphoric QG connection which attracted the attention of string theorists (QG is the raison d’etre for string theory) and which led Maldacena to formulate a conjecture involving a vague idea of supersymmetric string under the KK curling (with its even more vague idea of its QG content) on the dual AdS side in case one starts from a (supersymmetric) conformal field theory”.
For some reason also, quantum mechanics seems to be enough to understand black hole physics: “Of course one can use Bekenstein’s classical formula and equate it with this microscopically computed entropy to determine epsilon (I have not done this, but there can be no doubt that at this point the Planck length enters and determines the size of the vacuum polarization cloud). The calculations are in two papers […]”.
With Maldacena (and … and ….) literally on his knees, an alternative resolution of the apparent clash between quantum mechanic and general relativity was put forward by Wald: “His proposed solution was the start of the modern theory of QFT in CST in which the Lagrangian formalism is abandoned in favor of the adoption of the dichotomy of AQFT between the algebraic structure of QFT and the admissible states on such algebras.”
Numerous other advanced arguments seem to kill the claims 5) and 6) above. And for 7) I learned, that: “The localized algebras are monades with very different properties from algebras one meets in QM. There can be no doubt that the understanding of their positioning in a common Hilbert space will be an important step on the long way towards QG.”
But of course the “monad” (or, in biological terms, flagella) point of view also call into question whether string theory contains quantum field theory in its low-energy limit (8): “The message from this last case is that metaphoric arguments (e.g. looking at functional representations without actually doing the functional integrals) may turn out to lead to wrong results. Take for example the case of 2+1 dimensional QFT which have braid-group statistics. If the spin is anyonic (i.e. not semi-integer) the statistics is plektonic and the upholding of the spin-statistics theorem in such a case prevents the nonrelativistic limit to be a (second quantized) QM; it remains a nonrelativistic QFT. Only if one relinquishes the plektonic commutation relations, but preserves the anyonic spin one finds Wilczek’s anyons in the form of quantum mechanical Aharonov-Bohm dyons […]”, and then “The message from this illustration is that a theory can only be asymptotically (e.g. for long distances) contained in a more fundamental one if their structures harmonize.”
But the flagella (monads) also kill the S-matrix arguments 9): “A much more detailed correspondence of Leibniz’s image of reality in terms of indivisible monades to the conceptual structure of particle physics is provided by the algebraic setting of QFT (AQFT). If one identifies Leibniz’s monades with copies of the unique hyperfinite type III_1 factor algebras then it can be shown that any QFT permits a faithful encoding into the relative positions of a finite number of monades”.
At this point I started thinking: is this all a joke? Was I being fooled? Staring a the screen I was wondering whether or not I had really been fooled. On the one hand, if I wasn’t fooled, then this paper was serious, hence I was fooled by my understanding of physics. But if I was fooled, then I did get what I expected from BS, so in what sense was I fooled?.
Then suddenly I realized, that I had seen this text before, but just in another (isomorphic) disguise. It was the famous “Sokal hoax”, a hoax paper published by physicist Alan D. Sokal in 1994, entitled “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”. (Sokal’s hoax served a public purpose, that of attracting attention to what Sokal saw as a decline of standards of rigor in the academic community; for this reason, Sokal’s text was “liberally salted with nonsense”). For example, quoting from Sokal:
“In mathematical terms, Derrida’s observation relates to the invariance of the Einstein field equation […] under nonlinear space-time diffeomorphisms (self-mappings of the space-time manifold which are infinitely differentiable but not necessarily analytic). The key point is that this invariance group “acts transitively”: this means that any space-time point, if it exists at all, can be transformed into any other. In this way the infinite-dimensional invariance group erodes the distinction between observer and observed; the [pi] of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone.
“It is still too soon to say whether string theory, the space-time weave or morphogenetic fields will be confirmed in the laboratory: the experiments are not easy to perform. But it is intriguing that all three theories have similar conceptual characteristics: strong nonlinearity, subjective space-time, inexorable flux, and a stress on the topology of interconnectedness.”
So, was I fooled or not?