That has nothing to do with the measurement problem. Also, the measurement problem is only a problem of the Copenhagen interpretation. It doesn't exist in the many worlds interpretation.
Doesn't many worlds require branching into numbers of branches that would in some cases be irrational numbers? And you have to have some kind of index on the branch to make some of them physically distinguishable enough to still maintain probability. If equivalent branches are in there it's hard to explain how a 75%/25% branch would be distinguishable as a probability to an observer without some kind of extra index like information that has them land in the 75% more often. ( https://en.wikipedia.org/wiki/Many-worlds_interpretation#Pro...)
> That has nothing to do with the measurement problem.
He refered to I think the Diósi-Penrose model, where it would:
https://en.wikipedia.org/wiki/Di%C3%B3si%E2%80%93Penrose_mod...
But on the other point, how can there be an irrational number of branches to sample these statistics from? I just can't visualize the type of structure that would have that but I'm sure it is more subtle. I've heard the branches aren't branches under MWI but instead are something more continuous and I guess I don't understand it at that point.
Precision measurements by satellites around Earth and spacecraft scattered around the solar system reveal the nonlinearity of gravitation, as do precision measurements of systems like Hulse-Taylor and PSR J2222-0137.
A linear superposition law for gravitation is consequently unavailable - again, this can be seen in the solar system, where a linear superposition model helped find a real mass (Neptune, where ultimately the telescope targetting was driven by Urbain Le Varrier's detailed study of the orbit of Uranus in the 1840s, assuming the validity of Newtonian gravitation), but misled astronomers into decades of futile searches for "Vulcan", a hypothetical body inside Mercury's orbit.
There are a bunch of ways one can capture the nonlinearity of observed gravitation. A nice slogan: gravitation self-gravitates. A nice theoretical framework: Newton-Cartan gravity is great for exploring the failure of linear gravity. An easier theoretical approach: the relativistic two-body effective radial potential energy <https://en.wikipedia.org/wiki/Two-body_problem_in_general_re...> or less encyclopedically <https://spaceengine.org/articles/the-anomalous-advance-of-th...> where you can see the same effective potential term written slightly differently, with more about Mercury's orbit.
Quoting the latter:
Again I don't want to get lost in math, but it's worthwhile
just to look briefly at what the math is saying here.
Notice this still has the exact same two terms from the
Newtonian effective potential: an attraction that goes as
-1/r, and a repulsion that goes as +1/r^2. But a new term
is added: another attractive term that goes as -1/r^3. This
means that at very small radii, the -1/r^3 term dominates,
and gravitation becomes attractive again, dominating even
over the centrifugal effect of your orbital velocity.
No linear theory of gravitation is viable for known planetary and astrophysics. At best one can come up with a quasi-linear theory.
This is calculationally unfortunate: solving the full nonlinear Einstein Field Equations exactly is fiendishly hard. Where one can use a linear approximation, essentially every physicist would choose to do so. Indeed, Einstein invented linearized gravity (and various other approximation techniques). Unfortunately, linear theories of gravity can only ever be approximate, as they fail to deal with multibody systems, systems where orbital velocities are even only thousands of kilometres per second, where one wants to trace out radiation (including gravitational radiation), and so forth. Convincing proof of incompatibility between any possible linear theories of gravity and numerous observed physical orbits have been known since the 1960s. Roman Sexl did some really interesting work (alone and with collaborators like Otto Nachtmann) in that area in that decade.
These days one can turn to box 7.1 (sec. H) of Misner Thorne & Wheeler as a textbook starting point.
None of this really has anything to do with quantum mechanics, except with respect to a correspondence principle (e.g. Fraunhofer-like spectral lines have their origin in quantum mechanics, and we can see how gravity rather than just motion affects them).