JI/poly = MIP* = RE?

Recently, the string theorist Leonard Susskind proposed a new computational complexity class, "JI/poly", which includes all computations that can be performed in polynomial time by "jumping into" (j.i.) a black hole. We should also bear in mind his "ER=EPR" work with Maldacena, in which a wormhole is actually two entangled black holes. There is interest in the scenario in which an observer enters each black hole, and can never make it out the other side (this is for the case where the wormhole is non-traversable), but the observers can briefly meet inside the wormhole. I think JI/poly is meant to apply in scenarios like this. 

(Susskind also seems to say that the length of a wormhole has something to do with quantum computational complexity. This may be a holographic statement - that the length of the wormhole has something to do with the computational complexity of processes in its nongravitational dual. I don't have any opinion or use for this idea yet, but I mention it here for future reference.) 

Also recently, and closer to the mainstream of quantum gravity research, Witten et al proposed "an algebra of observables for de Sitter space" (finding observables for de Sitter space has been on Witten's mind for at least twenty years). They mention that this is a Type II1 von Neumann algebra (the algebra for an ordinary, nongravitational quantum field theory in flat space is Type III). 

This rang a bell for me, and indeed, there is an old conjecture in the theory of von Neumann algebras, due to Connes. Apparently the conjecture boils down to asking whether entanglement created by tensor products, is capable of approximating, arbitrarily closely, all forms of entanglement that can be created by commuting operators. This conjecture was falsified in 2020, as a corollary of the result in complexity theory that "MIP* = RE". 

MIP* is the set of computations that can be performed by two "provers" that cannot communicate, but which share an "infinite" amount of entanglement. RE is the set of "recursively enumerable" decision problems. This means there's a program which eventually lists every entity with a given property. So if you want to know whether entity X has property Y, and if there is a program that lists everything with property Y, then you can run the program and wait to see if X ever turns up in the list. Unfortunately, it could take a really long time for X to show up, and in general, you have no way of knowing if X ever will show up. 

But what MIP* = RE seems to mean, is that if X is in the list of entities with property Y, two infinitely entangled provers can prove it to you, in polynomial time. This is surprising because RE includes decision problems where it can take arbitrarily supra-exponential time for X to show up in the list. The provers, however, have infinite entanglement to work with - the equivalent of infinitely many entangled qubits - and that allows them to overcome the classical time complexity. 

I was just re-reading the thread on Scott Aaronson's complexity blog announcing the result, reliving the struggle of the commenters to understand what it means to have two provers that can't communicate but which have infinite entanglement - and suddenly I thought: that sounds like the two entangled black holes, in the Maldacena-Susskind model of a non-traversable wormhole! The observers can't pass through the wormhole - this is the counterpart of being unable to communicate - but if they both jump in, they can meet in the middle - something made possible by the entanglement of the black holes, since that is what creates the wormhole bridge. 

Does it mean that JI/poly = MIP* = RE? At least for the specific case of "two observers meeting in a non-traversable wormhole"... And what about the work by Witten et al? Well, they consider the case of two "static patches" in de Sitter space. Perhaps the two patches are analogous to the two event horizons of the non-traversable wormhole... 

I still have a lot to learn about all this, but I was sufficiently excited by the connection, that I decided to blog about it right away. :-) 

GU and MOND

I have been wondering whether one could obtain bimetric MOND from a GU-like theory. 

In addition to ordinary matter and metric, bimetric MOND has an extra "metric" (which does not interact with ordinary matter, but which may or may not interact with "twin matter"), and an interaction term connecting the two metrics, built from the difference between their Levi-Civita connections, which modifies the Newtonian limit. 

GU, meanwhile, features an extension of the usual gauge group by translations in the space of connections. I am still puzzling over the details, but a difference of connections shows up. 

I also need to better understand torsion (in GU and in GR). 

G. U.

In the previous post, I mentioned some technical evidence that string theory is the right approach to quantum gravity (namely that the threshold to preserve "cosmic censorship" of naked singularities, is provided by the weak gravity conjecture). Another example of such evidence is that string theory predicts the same corrections to black hole entropy, as the semiclassical approach to Euclidean quantum gravity. 

On the other hand, asymptotic safety did manage to predict the Higgs boson mass, and apparently passed one technical test that it shouldn't have (the two-loop counterterm). And on the empirical side, MOND makes a few successful predictions that don't come naturally from dark matter. 

Meanwhile, we have a new theoretical contender: "geometric unity", finally the subject of a technical paper this year, after years of secrecy. GU's creator is using his theory as part of a very public attempt to create an Internet-based intellectual counter-establishment outside of academic groupthink, so it's a little controversial. 

Nonetheless, now there's a paper, it is possible to judge the theory on its own merits. I can report that it's based on a few nice concepts, but it remains to be shown that the concepts can be realized mathematically. (There is already a "response to GU" paper which doesn't engage with the core ideas, but does state some of the technical barriers that will need to be overcome.) 

Weak gravity, p-adic gravity

Quantum gravity is a surprisingly diverse subject, and it can be hard to know where to focus. But here are two recent papers that seem guaranteed to be noteworthy.

"Further evidence for the weak gravity - cosmic censorship connection". This coincidence is evidence that the quantum-gravity paradigm employed is the right one; if it's wrong, why would the coincidence exist?

"General relativity from p-adic strings". Apparently a refinement of another "coincidence", the well-known connection in string theory between conformal symmetry of the worldsheet, and general relativity in space-time; but now for a worldsheet based on p-adic numbers.

Paradox men

While this blog hibernates, I will note the recent deaths of Joseph Polchinski and Stephen Hawking, both known for "paradoxes" concerning the evaporation of black holes (though Polchinski will really be remembered for D-branes).

(The Paradox Men is an American time-travel novel that preceded both of them.)

Initial conditions

Since June 2017, Sabine Hossenfelder has hosted a dialogue/debate between Tim Maudlin and "black hole guy" about how to quantize gravity. (The precipitating post was made in May, but BHG did not show up until June.)

It is now February 2018 and I wonder how much longer the thread will remain open. So I have created this blog as a place where discussion can continue, should that be necessary. My primary interest is in the orthodox path to quantum gravity represented by BHG, but certainly the great debate can continue here, should it ever need a new home.