# Naked singularities, space invaders, and the quantum

### Quantum mechanics from general relativity via naked singularities and stochastic mechanics?

Greetings to all readers and subscribers, and special greetings to the paid subscribers!

Please scroll down for the main topic of this newsletter. But first:

On Feb. 19 I gave an online talk for Space Renaissance. I elaborated on the cultural issues discussed in my book “*Futurist spaceflight meditations*” (2021). Then I discussed the long term future of space expansion and elaborated on its spiritual implications.

This was a blunt and provocative talk, with the gloves off. I guess I should apologize to the authors whose books I called BS, but the thing is, those books are well researched and written but the decel program they defend is really BS, and we must say so. Occupy Mars!

Here’s the slide presentation I used.

I’ve been reading an interesting paper mentioned by Sabine Hossenfelder on X. The paper, by Pankaj Joshi and Sudip Bhattacharyya, is titled “Primordial naked singularities.” The thesis is that primordial naked singularities, or particle creation near them, could be (or contribute to) dark matter.

Naked singularities are mathematical solutions to Einstein’s field equations of general relativity that are not hidden behind event horizons. A naked singularity is “not clothed in the usual event horizon blocking any undetermined surprises from view,” and therefore “space invaders” can appear anytime [Rickles 2016]. Primordial naked singularities (PNSs) are naked singularities formed, perhaps in abundance, in the early universe.

Pankaj Joshi works in general relativity and cosmology. Among other works, he has written the books “*Gravitational Collapse and Spacetime Singularities*” (2007) and “*The Story of Collapsing Stars: Black Holes, Naked Singularities and the Cosmic Play of Quantum Gravity*” (2015).

See my post “No to cosmic censorship! Singularities have a right to go naked” for background and references (and add Joshi’s books to the references).

The paper made me think of an idea that comes to my mind now and then: perhaps naked singularities are sprinkled all over space and time, and this could “explain” (so to speak) quantum mechanics.

My reply to Hossenfelder’s X post: Has anyone suggested that naked singularities are sprinkled all over space and time *and therefore* determinism is broken all the time everywhere? Has anyone suggested that this could “explain” quantum mechanics?

Let me sketch this (very speculative) idea.

A naked singularity would break Laplacian determinism because unexpected particles might pop out of the naked singularity anytime like “rabbits popping out of a hat” (Joshi 2015). So a naked singularity would inject a halo of uncertainty, so to speak, into the universe. Suppose naked singularities are sprinkled all over space and time like fairy dust. Then there would be a permanent mist of uncertainty all over the universe.

Could this help make sense of quantum behavior?

Edward Nelson sketched a stochastic formulation of quantum mechanics based on “a kind of Brownian motion that agitates all particles of matter” [Nelson 2001]. Nelson assumed that all particles undergo this motion and derived the Schrödinger equation of quantum mechanics. He soberly resisted the temptation “to think of a material model of the aether and to imagine the cause of the motion to be bombardment by grains of the aether.” But why not? In later works Nelson tried to develop the theory, but then he considered the theory unrealistic because it would have to include nonlocal aspects [Nelson 1985, Nelson 2012].

To me, nonlocality is not a problem but just the way things work. So it seems plausible to me that some kind of background substrate induces fractal Brownian-like motion at all scales in ways that are not yet understood, and quantum behavior follows. And since quantum mechanics has nonlocal aspects, which is confirmed by experimental evidence, any theory from which quantum mechanics can be derived would have nonlocal aspects as well. Nelson’s stochastic mechanics, I think, goes a good part of the way toward deriving quantum mechanics from a physical model and making intuitive sense of quantum mechanics.

In a recent review of stochastic mechanics, Folkert Kuipers summarizes recent research and suggests that particles interact “with an omnipresent background field” whose dynamics could “be described by some (non-)deterministic physical laws” [Kuipers 2023].

I’m having fun with the idea that the omnipresent background field could be an ocean of naked singularities and particles that pop out of them in essentially random ways (as far as we presently know).

Joshi and Bhattacharyya only say that PNSs “are a viable dark matter candidate and could coexist with some other dark matter candidates.” But if dark matter is entirely made of PNSs, then PNSs could be distributed with very high density all over the universe. If the average separation between PNSs is very small, then all particles would be continuously bombarded from all directions by “space invaders” [Rickles 2016] that pop out of PNSs randomly. The paths of all particles would cease to be smooth one-dimensional paths and become fractal paths with fractal dimension two, just like Brownian paths [Falconer 2014] and Feynman’s “typical paths of a quantum-mechanical particle” [Feynman 2010]. Stochastic mechanics, and therefore much of quantum mechanics, would follow.

It would be interesting to develop a statistical model of this background ocean and link it to the developing theory of stochastic mechanics. This would be a nice way to derive (something like) quantum mechanics from (something like) general relativity. Perhaps the weirdest aspects of quantum mechanics (nonlocality, entanglement and all that) could be derived from the yet unknown dynamics of the background.

I guess this idea must have been considered but I haven't been able to find any reference. Should I think of a catchy name and promote it? But no, this idea would be canceled if it comes from a mad scientist like me, better let real scientists have fun.

I exchanged emails with Joshi and Bhattacharyya to ask questions about their paper and suggest this idea. I understand that their research program is still in its very early phase, and I can’t wait to read new papers.

The devil is often in the details. Where do all those tiny naked singularities come from? Perhaps they have always been there (I guess this would be the simplest assumption to start with). Perhaps, as Joshi and Bhattacharyya suggest, primordial naked singularities were formed in the very early universe alongside primordial black holes. Very light primordial black holes would likely evaporate away, but the evaporation of a black hole “might leave behind a tiny naked singularity” [Thorne 1994]. The implosion of a gravitational wave might leave behind “an infinitesimally tiny naked singularity” [Thorne 2014].