Woit plus Weinstein

This is my latest fuzzy thought... Woit's theory ("Euclidean twistor unification") is a form of chiral graviweak unification. In such theories, a four-dimensional rotational symmetry is factored into left-handed and right-handed components, which become the gauge symmetries of the weak force and the gravitational force respectively. Woit goes further, considering a particular quotient bundle in twistor space, in order to obtain the hypercharge and color gauge symmetries as well. 

Some things are lacking in Woit's theory - like fermions, and three generations. But let's suppose he does have a way to obtain gravity and the standard model gauge fields, by looking at the twistor space of a 4d manifold in a particular way... If we switch back to Weinstein's Geometric Unity, it embeds a 4d manifold into a 14d manifold which is actually the metric bundle of the 4d manifold. Then we are to have a 14d Yang-Mills field coupled to the 4d manifold by a "shiab operator" in such a way as to somehow give us 4d gravity, and a 14d Dirac field that in 4d will give us two of the three fermion generations (with the heavy third generation to come as a piece of a 14d Rarita-Schwinger field). 

What interests me is whether Woit's construction can be obtained as a subset of Weinstein's. One reason to consider this, is that Weinstein also talks about obtaining gravity from an SL(2,C) subgroup of his complexified 14d gauge group - a group which also features in some chiral approaches to gravity. Unfortunately it is unclear to me how this related to the shiab operator, which is to mimic, for the 14d gauge field, the Ricci decomposition of the 4d metric. 

Schwarzschild mereology

Earlier this year it was claimed that Schwarzschild geometries (i.e. the classic black hole geometry) can be obtained by assembling a collection of Reissner-Nordstrom black holes held together by "struts" that resemble negative-tension strings. This is therefore a model for the microstates of a Schwarzschild black hole. 

(1) There's a somewhat fringe theory that black holes contain negative pressure that contributes to dark energy. I would want to look at that idea, also negative branes (associated with altered spacetime signatures), also how black holes are obtained in Matrix theory and Tom Banks's musings on how to obtain de Sitter space in a similar way. 

(2) As far as I know, we don't know how to obtain RN black holes in string theory? They can be approximated by JT gravity but UV completion not known. 

Nebulous

I had a thought today: what if Eric Weinstein's Geometric Unity, has a formulation as complex E8 gauge theory in 14 dimensions, coupled to a brane whose worldvolume theory is Gunaydin's 4d octonionic magic supergravity? The rationale for this being the 14-dimensional grading of E8(C), something which Michael Rios told me about years ago. 

It's unlikely, but a concrete speculation like this, is a way to get a handle on several otherwise nebulous possibilities. 

Wide binaries

 This is a placeholder post, for discussion of wide binaries. 

Logarithmic potential

I have learned that MOND can be obtained from a potential that adds a logarithmic potential to the usual inverse-square potential, with the logarithmic potential dominating past a certain distance, and producing a 1/r force law. 

Also, while researching the history of neutrino theories of gravity (!), I ran across Chapter 2 of Feynman's rare "Lectures on Gravitation", in which he considers a peculiar three-way interaction, between two bodies and large distant masses, which produces a potential with a dominant logarithmic term (see equation 2.4.6). 

Could something like this give us MOND?!

Replicas

In real life, I am on a mission which led me to move halfway around the world for reasons having nothing to do with quantum gravity, though of course the issues interest me. So imagine my surprise when on local TV yesterday, there was a news story announcing a new institute intended to solve quantum gravity.

Looking at the founding conference, it seemed largely to be about a few rich guys supporting the work of non-string-theorists who are already well connected academically. So it's unclear whether they would ever support my own physics research. But I will probably investigate more about how the sponsors got together, simply to understand philanthropy and the tech scene here, for the sake of my other mission.

I did look into the personal quantum gravity theory of the main physicist among the local organizers. At first it seemed a peculiar and arbitrary exercise in having gravitational interactions between different branches of a superposition. Too bad, I thought, that all that money is going to support such an unmotivated hypothesis.

But then I remembered the appearance of  'replica' space-times, connected by wormholes, in some fashionable recent theoretical studies of the black hole interior. So maybe it's better motivated than I thought.

In other news, I actually linked to this blog, in a new discussion of the "JI/poly" scenario at Scott Aaronson's blog, but unfortunately everyone was distracted by philosophy-of-mind issues and didn't address more technical matters, like whether the time it takes to get out of a traversable wormhole nullifies any computational advantage derived from working inside it.

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. :-)