Eric Weinstein's invisible theory of nothing

On Friday, I received an irritated message from Mel B. who had read articles in the Guardian claiming that Eric Weinstein found a theory of everything or something close:

Roll over Einstein: meet Weinstein (by Alok Jha)

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Eric Weinstein may have found the answer to physics' biggest problems (by Marcus du Sautoy)

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Geometric Unity (a lecture at Oxford that no physicist attended)

First, the puns involving names emulating Einstein are extremely far from being new to me because as the most successful Czechoslovak debunker of these new Einsteins (I mean anti-relativity cranks in this particular case), I've spent quite some time with the Slovak crackpot originally named Arthur Bolčo who also wrote the book Arthur Bolstein: An Ordinary Collapse of an Extraordinary Theory (which had both Einstein's and Bolstein's photographs on the cover, cute).

Now, Weinstein is a smart guy, a likable figure, a hedge fund speculator, the father of the MathWorld encyclopedia later run on Wolfram's domain (mistake! A different man, see the comments), and a discrete physicist close to folks like Edward Frenkel, a mathematician at Berkeley.

But the stories in the Guardian are just completely insane because they have absolute no basis.




This aspect of the story was nicely discussed by Jennifer Ouellette's blog entry "Dear Guardian: You’ve Been Played". Her blog, Cocktail Party Physics, has been incorporated into the website of a once nice American science magazine.




Eric Weinstein doesn't seem to have written a physics paper in his whole life (if we don't count his bizarre 0-citation PhD thesis) and this particular new theory of everything isn't described in any paper – not even an informal preprint – that anyone has seen. He was just invited by a buddy to give a seminar that no one attended and no one who knows similar things was invited to, in fact.

So it seems like another self-evident case of nepotism, self-promotion, unprofessionality of the journalists in the Guardian, and "science" run by press conferences. Even Nude Socialist's Andrew Pontzen concluded that Weinstein's theory of everything is probably nothing; see also a similar criticism by Spinor Info. I am not gonna speculate on whether or not Eric Weinstein has paid for the self-promotion but I think that it would be legitimate to speculate because there's quite some case for this hypothesis. It's comparably conceivable that the whole effect may be explained by the journalists' gullibility and stupidity and nothing else.

I don't know the content of the Oxford seminar, I haven't seen any paper, and I don't even know whether a paper will ever exist at all but building on some rumors, it seems that his work is another episode in the widespread confusion about the "graviweak unification". Papers by authors by Garrett Lisi – and in the case of the "TOE" papers, even papers by folks like Fabrizio Nesti (who wrote the JHEP \(\rm\LaTeX\) macro and added even some papers on matrix string theory, among others; despite his "priority", Nesti is less famous than Lisi because he's a sailor, not surfer) – are mixed sequences of mistakes, blunders, errors, misunderstandings, and – in the best passages – unjustified hopes.



I guess that Rammstein is a relative of Einstein, too. It's cool music I only began to like less than 10 years ago under the influence of friends JB and OK.

There are lots of lethal flaws in these papers each of which is sufficient to kill the idea. But the most general theme, the "graviweak unification" i.e. the unification of the electroweak and gravitational interactions at the level of spacetime fields, is just totally hopelessly wrong. There can't be any "graviweak unification".

It seems rather clear to me that all these authors are confused by the apparent similarity between the local Yang-Mills groups of gauge theories such as \(SU(2)_W\times U(1)_Y\) for the electroweak theory on one hand; and the local Lorentz group such as \(SO(3,1)\) acting on vielbeins \(e_\mu^a\) in the tetrad formalism describing the general theory of relativity i.e. gravity on the other hand.

These groups enter the dynamics differently but these differences could perhaps be due to some symmetry breaking (and even the difference between one group that is compact and another group that is not could turn out to be harmless, perhaps).

But the key fact that those people completely miss is that the \(SO(3,1)\) local Lorentz group is in no way the key local symmetry principle underlying general relativity in its "covariant" description. Instead, it's the diffeomorphisms that are the key symmetry. And diffeomorphisms are completely different transformations than the local Lorentz symmetries! Diffeomorphisms act like\[

\phi(x,y,z,t)\to\phi'(x,y,z,t) = \phi(x',y',z',t')

\] on the scalars and I want to avoid descriptions how tensors transform because you should know it. At any rate, the new value of a field at a point after the action of a diffeomorphism depends on the value(s) of the field at another point before the diffeomorphism acted. On the other hand, the local Lorentz symmetries – much like the Yang-Mills symmetries – only transform the fields at the same spacetime points into each other. The counterpart of the transformation above would need no primed coordinates \(x',y',z',t'\).

These are completely different transformations and the local Lorentz transformations are really unnecessary, optional. We may do general relativity without them. On the other hand, the tetrad formalism of general relativity requires both the local Lorentz symmetry and diffeomorphisms. What's essential for gravity are the diffeomorphisms which are completely different beasts than the local Lorentz transformations. Their generators are given by the stress energy tensor \(T_{\mu\nu}\) which has two vector indices (spin 2), unlike the generators of Yang-Mills-like symmetries \(J_\mu\) which are currents with one index (spin 1 of the gauge bosons).

There can't exist any purely field-theoretical unification of spin-1 fields and spin-2 fields (and of the corresponding symmetries) in the same spacetime that would be described by field theory. Only string theory and its diverse descriptions may achieve such a unification. They do so by attributing an internal structure of a sort to the particles including the messengers – for example, it's the string that may have internal vibrations and those may change the spin of the resulting particle, too. In this unification, one immediately generates an infinite tower of new states with arbitrarily high spins aside from \(J=1\), \(J=2\), too. And if we're "lucky", the excitations of the extended objects interact consistently, avoid divergences and anomalies, agree with the physics of gauge theories and general relativity. Only string theory in its different manifestations has been "lucky" so far and it seems likely that no other theory will ever join this "lucky" club.

The reasons why gravity can't be unified with the Yang-Mills forces in the naive, field-theoretical way is no string theory. In fact, it's not even rocket science. I find it strange that these men can't understand the reasons. I find it shocking that they still can't penetrate these simple things and isolate the simple mistakes they've been doing for years.

You may perhaps define some equations of motion that unify the (compact) Yang-Mills groups of the Standard Model (or similar ones) with the (noncompact) local Lorentz symmetry but the resulting theory will still have nothing whatsoever to do with gravity because the natural local transformations that allow us to write gravity covariantly are diffeomorphisms, not local Yang-Mills-like symmetries. Moreover, actual physicists have known for quite some time that in the real world, the unification of gravity with other forces critically depends on quantum mechanics which is why arbitrary games with the classical Lagrangians are no good.

Eric, Fabrizio, Garrett, please try to wake up and stop with this immensely stupid crackpottery and the embarrassing promotion of this crackpottery in the media!

14-dimensional fiber bundle

Incidentally, some sources suggest that Weinstein wants to construct his "theory of everything" out of a 14-dimensional bundle obtained by placing the 10-dimensional space of possible values of the 10-component metric tensor \(g_{\mu\nu}\) at each point of the 4-dimensional spacetime. That's a fun thing to present the identity \(10+4=14\) but it's otherwise completely empty. If you specify how many dimensions a theory should have, it is extremely far from actually having a theory – knowing a consistent description of the interactions of some particle, fields, or other objects in a given spacetime. Moreover, in some reasonable clarifications of the 14-dimensional theory, the 10 dimensions are spurious and the theory is still the same 4-dimensional theory with 10 fields we have known as general relativity.

Independently of that, there can't be any natural theories with a stable enough spacetime in 14 dimensions.