Persistent Inconsistent

On the Frauchiger-Renner inconsistency theorem

A little treat here for anyone reading this channel who has a passing interest in fundamental physics. Not your cup of tea? Not so delicious? OK, well I’d think it was a treat if I was a young kid growing up with a persistent need to not follow the mainstream for some bizarre and knowingly economically debilitating reason.

My T4GU blog writing probably will come across as too irreverent and comedic for serious physicists, but I hope someone has a glance and offers some push-back. I really do want to know if there is a no go theorem for T4G (Topological 4-Geon Theory).

Background to F-R

Back around 2018, Daniela Frauchiger and Renato Renner wrote a fairly high impact paper (here) showing most interpretations of quantum mechanics fail to satisfy one of three very reasonable scientific standards. These are named Q, C and S.

• (Q): An agent (aka. a QM-algorithm programmed computer) can be certain that a given proposition holds whenever the quantum-mechanical Born rule assigns probability 1 to it).

• (C): Demands consistency, in the sense that the different agents' predictions are not contradictory.

• (S) The requirement that, from the viewpoint of an agent who carries out a particular measurement, this measurement has one single outcome.

What does it mean for a dumb computer to be “certain”? This is actually not a trivial question, and in a nice talk Renato Renner explains that you should feel free to insert any reaosnable definition of “certain” you like, e.g., everyone is honest, computations have no bugs, Born Rule probabilities yield 1, &c. There are a few other nuances about the gedankenexperiment that make listening to Renner’s talk a non-boring lunchtime of entertainment.

The proof uses a type of Gödel-Cantor diagonalization: use quantum mechanics rules to model quantum mechanics (on a classical computer? — this bit was unclear, I think you are supposed to imagine the computers are actually fully quantum). The introduction of programmed computers spitting out strings using only the algorithm of quantum mechanics is to avoid philosophical fluff talk about “conscious agents”. There is no need for such things in this gendankenexperiment. Although as some youtube posters will complain, “Who built and programmed your computer?” LOL. Nerds, huh.

The TLDR; is that I try to write about what T4G would conclude from the F-R inconsistency. It is not difficult. T4G says quantum mechanics is not universal. So we reject (Q) and happily go along our merry consistent way. The fun in my blog piece (here) is in discussing why, and in the process dunking on a few other mainstream QM ideologies.

Background to T4G

(This is to save you time, to warn you against clicking away to read the fun stuff.)

T4G theory seeks to use Gravity to derive all of quantum mechanics. The humility-boson is not a fundamental field in our theory. For the cosmology I find we can borrow almost whole cloth from Turok & Boyle’s CPT-Symmetric universe conjecture (which is phreakin’ awesome).

The catch for T4G is that we cannot obviously use classical GR. But quantum mechanical logic of measurement propositions (a nondistributive orthomodular lattice of measurement propositions) follows naturally from nonclassical GR, and a particularly nice minimalist extension: one only needs to admit spacetime has nontrivial topology around the Planck scale. Wormholes. That is the required nonclassical GR extension. (I also think it good to include conformal symmetry in GR, which is best handled imho using the gauged gravity approach in the spacetime algebra framework — the graded Clifford algebra Cl(3,1).)

This implies closed timelike curves (CTCs) exist (but they are not necessarily traversable by matter). They are also not classically traversable, so there is no ubiquitous FTL effect. To be sure, there is FTL and this is why we get a quantum theory, but it is constrained to the quantum level, naturally (by Geroch topological censorship).

How this relates to F-R is that in this GR+CTC=QM picture we understand quantum mechanics is inapplicable for a large system where sufficient entanglement structure (the ER bridges) has been broken that interference effects (and nonlocal correlators) can be ignored. However, this is spacetime topology, not some mystical mumbo jumbo like de Broglie-Bohm HV’s or Many Worlds. If you like, in T4G theory there are local hidden variables, but if you do not account for the ER=EPR bridges they appear non-local, and if you really ignore them then they are also hidden.

End of tldr transmission.