[mr_mitm]

They are singularities in the framework of general relativity, i.e. while ignoring quantum mechanics. I think most people expect the right version of quantum gravity to make the singularities go away, but studying classical GR is worth it on its own, so it's often ignored like in this statement you quoted.

[goatlover]

What if gravity is non-linear and thus collapses the wave function? I think Penrose has suggested gravity as an objective collapse interpretation. The measurement problem still hasn't been resolved, but we observe a classical world around us, despite the fact that decoherence simply spreads the superposition of interacting quantum systems to the world. Gravity could be what prevents the linearity of quantum systems from putting the entire universe into superposition.

[mr_mitm]

Gravity is non-linear (as in: the Einstein field equations are non-linear differential equations).

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.

[cma]

> 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...

[GoblinSlayer]

Born rule doesn't need index, it needs statistics of a sequence of measurements, then statistics is rationalized as a result of a stochastic process.

[cma]

In that link that says that was Everett's initial attempt to solve but it has been debated and extended. I only have a podcast understanding of it, and have heard the popular proponents of many worlds like Sean Carrol say that is the biggest problem that needs more development, he has his own self-locating thing but there are many other approaches.

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.

[GoblinSlayer]

Wikipdeia references https://arxiv.org/abs/0905.0624 and first thing I noticed in section IV the author incorrectly calculates copenhagen prediction (because probabilities are counterintuitive), but correctly everettian prediction (because marginal outcomes are obvious there) and claims this discrepancy disproves MWI, he conveniently forgets about empirical equivalence of interpretations, so that it's easier to make an error and get different predictions. Then makes incorrect claim about MWI. Any given observer will probably observe confirmation of Born rule due to the law of large numbers.

[GoblinSlayer]

The structure of superposition is given by solution of the Schrodinger equation. It's often continuous, e.g. electron's s orbital in atom is a continuum of coordinate eigenstates. In this case a discrete sum is replaced with an integral and Born rule becomes a function on this continuum, but a discrete case can be easier to understand, so I recommend to start with that. The proof follows the law of large numbers https://en.wikipedia.org/wiki/Law_of_large_numbers

[goatlover]

Gravity as in the actual force or field, not the current equations. You mentioned quantizing gravity, a few physicists like Penrose doubt it can be done. MWI is not a consensus, and there are more than two interpretations. Objective collapse theories have also been proposed, at least one involves gravity as the mechanism.

[raattgift]

The nonlinearity of gravity is obvious even in the solar system - it was discovered because Mercury's orbit, when described with the linear theory of Newton's universal gravitation, behaved as if there were an additional hidden mass between its orbit's periastron point and the sun. Or, if you prefer, summing all the sources of gravitation in the solar system is insufficient for describing all the observed orbits in the solar system. (Indeed, even if you summed all the sources of gravity in the galaxy, you wouldn't get the evolution of the relatively eccentric elliptical orbit of Mercury right.)

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.  

The increased attraction mimics an additional mass in a linear theory.

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).

[GoblinSlayer]

Decoherence splits your state into superposition of several coherent states then you observe one classical result in each state in superposition, that's why it looks classical.

[nathan_compton]

As far as I know the limits on physical collapse theories are extremely strong and there are some reasonably good philosophical reasons to doubt them as well. I don't have the text in front of me at the moment but Aaronson's Quantum Computing Since Democritus has a section on this, I think. If physical collapse were true then the implications for quantum computing would beggar belief. P=NP stuff.