Tuesday, May 11, 2010

SUGRA, black holes, and quantum information

CERN Courier has brought us a new fun article by Mike Duff:
Black holes and qubits
Yes, I took the Wikipedia picture.

In recent years, Duff has been working on the entropy of various M-theoretical and SUGRA black holes with many types of charges. The very formulae for the black hole entropy must respect and do respect the U-duality, a symmetry of the theory, so they know about various cool exceptional algebraic structures such as exceptional Lie groups, octonions, GHZ states, and hyperdeterminants.

Some of the very same formulae appear in quantum computation. That makes it almost inevitable for the string theory techniques to tell you something new about the quantum computers - and vice versa. For example, Duff explains a cool realization of some qubits' properties in terms of brane intersections. This strategy also leads to the quantum version of Shakespeare: to wrap or not to wrap, that is the qubit. ;-)

Also, he proposes some "supersymmetric" extensions of some qubit rules - new possible quantum algorithms inspired by high-energy physics; time will show whether they're excessively viable.

Duff believes that this work will also "re-energize" concepts such as octonions in physics that have been considered a "lost cause" for years by many people. Well, I personally think that the octonions' role in some "exceptional" places of physics has already been established, while their role at more general places - e.g. the replacement of complex numbers by octonions in all of quantum mechanics - has been pretty much ruled out. So I believe that the octonions' importance in physics will remain "limited".

Duff also discusses tests of string theory in general, and so on.

But there is one more important disclaimer concerning the relationship between the black hole thermodynamics and quantum information: it doesn't seem to be a full-fledged duality. The hyperdeterminant is a somewhat nontrivial mathematical structure. It's cute and we should be excited when we encounter it at several places.

But as long as it is just one formula, it doesn't allow us to calculate "anything" about quantum computers or "anything" about the behavior of black holes using the objects from the other side of the relationship. There's more physics than just the hyperdeterminant on both sides. The situation therefore differs e.g. from the AdS/heavy-ion duality where "all" the Green's functions on both sides - infinitely many functions - can be mapped and matched.

In particular, the entries that are substituted to the hyperdeterminant are charges on the SUGRA/black-hole side, and they are qubits on the side of quantum computing. It's not the same thing. Why?

There are also qubits on the black-hole side (although not "simply" separated from each other because black holes or other physical systems are surely not base-two quantum computers!) but the effective number of these black-hole qubits or the entropy increases as a power law with the black-hole charges while the hyperdeterminant formula makes the total number of states - the *exponential* of the entropy - to increase as the power law of the charges! So the role of the qubits, or the arguments of the hyperdeterminants, are "physically" completely different.

That's why it's not quite obvious that the appearance of the same algebraic structure *has* to be useful. But it may be useful, anyway. The "character" of objects and phenomena in physics is given by their mathematical properties. So if they have the same mathematical properties, they're the "same thing". Many people - and most people who dislike maths - misunderstand this basic point.

However, at the same moment, we must realize that one formula doesn't make *all* maths being equivalent on both sides. A superficial similarity of one aspect is very far from a full-fledged mathematical equivalence.

And that's the memo.

Bonus: Duff-Smolin debate

CERN Courier also recalls a debate between Mike Duff and Lee Smolin in 2007:
Transcript, audio, TRF.
Funnily enough, in the transcript, almost all moderately technical words such as quarks, leptons, Schwarzschild etc. are transcribed as "inaudible", while other physicists are spelled as Le Plas or Padolski, suggesting that the transcriber wasn't an expert, not even a fan of physics.

At that time, two crackpots who have lost their case in the court of science were pretty successful in getting excessively idiotic journalists to support their case - their desired transformation of physics as a hard science into another branch of politicized flapdoodle led by inferior minds - in the court of public opinion, as Mike Duff emphasized.

Of course, times have changed and everyone knows that Swolin and Smoit were just self-serving unproductive imbeciles, liars, and parasites who would mean - and who do mean - exactly nothing without the support of their fellow imbeciles in the media.

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