"Weak gravity" sometimes enforces "cosmic censorship"

Clarifying the truth value status of WGC, CCC, loop quantum gravity, and their relationships

Natalie Wolchover wrote a Quanta Magazine story

Where Gravity Is Weak and Naked Singularities Are Verboten

which is promoting some fun May 2017 work by Jorge Santos (Prof) and Toby Crisford (student, both Cambridge UK). I guess that just like in many other cases, the reason why a popular article was scheduled was that the February 2017 preprint (which has about 1 citation so far) has recently appeared in a prestigious printed journal:

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti–de Sitter Space (PRL; arXiv)

They considered GR coupled to electromagnetism – the Einstein-Maxwell system – in \(AdS_4\) and found a counterexample to the 1969 Cosmic Censorship Conjecture by Roger Penrose. It's the electromagnetic force that allows them to achieve the outcome (which Penrose considered forbidden) with the naked singularity. And they argue that exactly when the 2006 Weak Gravity Conjecture by ArkaniHamed-Motl-Nicolis-Vafa is obeyed, the cosmic censorship will be defended and the pathological singularity will be hidden within a black hole.




Well, I think that Santos and Crisford wrote that the inequalities for cosmic censorship and that of the weak gravity conjecture are only the same up to a numerical factor that may fail to be one, and that may fail to be theory-independent, so I think that the "precision" of the equivalence is overstated in Wolchover's article. But let's ignore this technicality: the rough claim is that the \(AdS_4\) theory coupling electromagnetism and gravity will be defended against the bad, naked singularity if and only if gravity is the weakest force (if there exist charged particles whose electrostatic force trumps the gravitational one).

But while Wolchover wrote a lot of interesting things nicely and accurately, there is some basic confusion about basic qualitative issues in her text, too.




So first, let's review some basics. When we formulated the Weak Gravity Conjecture, we had some evidence based on clever semi-heuristic arguments within general quantum gravity, sort of controlled gedanken experiments similar to those that Einstein and Bohr discussed in their debates about quantum mechanics. And we had anecdotal evidence based on the fact that the inequality seems to be obeyed in string/M-theory.

Even though Crisford and Santos used numerical techniques in GR, their addition to the support of the Weak Gravity Conjecture must be counted as another semi-heuristic argument, and an interesting one.

Our semi-heuristic arguments derived the Weak Gravity Conjecture from the requirement that black hole remnants must be absent; near-extremal charged black holes must be unstable; and gauge symmetries imitating the (forbidden in quantum gravity) global symmetries too well should better be banned. Some of the 300 followups have linked the inequality to some other interesting, well-motivated, and seemingly independent conditions.

Crisford and Santos add an exciting new one. If we had known about this calculation in 2006, their paper could have become another chapter of the paper and the list of authors could have had 6 members. ;-) If there are extra forces that are much weaker relatively to gravity, one may use them to form singularities – singularities unprotected by an event horizon. Many people generally believe that women on the street shouldn't ba naked, and neither should be well-behaved singularities in a well-behaved Einsteinian theory of gravity. Both assertions are somewhat normative in character; they haven't really been proven. But Crisford and Santos indicate that this claim about the "etiquette of singularities" isn't independent from some other, more justified rules in physics.

To derive the condition whether the electromagnetic force is stronger than gravity, as required by the ban on the naked singularities and by the Weak Gravity Conjecture, you need some kind of a unification of these two forces. Your theory should better agree that their strength may be "the same" in some correct quantification. So theories without any unification of gravity with other forces will almost certainly fail to enforce the Cosmic Censorship Conjecture.

Loop quantum gravity is an example. People who promote this šit have repeatedly said that you can just add electromagnetism on top of their infantile version of aether irrationally claimed to resemble Einstein's gravity and the coupling is unconstrained. If that's so, this LQG+Maxwell will sometimes enforce the cosmic censorship, sometimes violate it.

So Nima Arkani-Hamed is quoted as saying "If the weak gravity conjecture is right, loop quantum gravity is definitely wrong". Thanks for that, Nima. Well, Nima's thoughts about loop quantum gravity have been very similar to mine for decades but I am pretty sure that it's the first time you were told that Nima could dare to think that loop quantum gravity is wrong, not a real competitor.

Funnily enough, Lee Smolin, a loop quantum gravity dog, told Wolchover that "if the Weak Gravity Conjecture is true, there will be a loopy reason for it". This is just another amazing example of Smolin's brutally unscientific methodology. No derivation of the Weak Gravity Conjecture from loop quantum gravity is known and it seems almost obvious that none may exist because some constraint on the strength of the two forces requires some "unification" of these forces and loop quantum gravity's traveling salesmen generally say that the right theory, theirs, doesn't contain any "unification". So Smolin uses some hypothetical paper that doesn't exist and probably cannot exist in order to create the impression that in this cosmic censorship test, loop quantum gravity managed to tie string theory once again.

Sorry, it didn't. If cosmic censorship is viewed as a "nice thing", then the corresponding required inequalities have been shown to hold in string theory, but they haven't been (and they probably cannot be) shown to hold in loop quantum gravity. So the comparison of string theory and loop quantum gravity is surely not a tie. Like in dozens of previous comparisons, string theory won, loop quantum gravity lost, and you're just a pile of dishonest lying garbage, Mr Smolin. Unrealistic promises just aren't equivalent to results. And while people are finding interesting results, you have done nothing valuable in your life, Mr Smolin, while your demagogy only impresses the least demanding laymen if I avoid the term filth.

But I was actually shocked by a statement that Wolchover wrote herself, too:

Such an alliance with the better-established cosmic censorship conjecture would reflect very well on the weak gravity conjecture.

Oh, so the cosmic censorship conjecture is "better-established" than our conjecture? And you express this view in a popular article whose main purpose is to explain the new paper by Santos and Crisford? Let me mention that the first sentence in the abstract of the Crisford-Santos paper says:

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions.

So if you actually respect the results of the paper you were supposed to explain, the Crisford-Santos paper, the cosmic censorship conjecture isn't better-established. It is wrong. The folks found a counterexample. Wolchover is good but surprisingly, she was in a minority of writers who got this point incorrectly. Most of the dozen of so of news reports about the Santos et al. paper did realize, even the title, that they have invalidated Penrose's conjecture.

Theirs is really very far from the first counterexample to Penrose's conjecture. First, the original version of the "cosmic censorship conjecture" was stronger and was shown to be invalid very quickly. So it was weakened – not really once, in fact – and that's why Crisford and Santos, as well as others, only deal with some "weak cosmic censorship conjecture". But even this weakened version has been known to be violated above four spacetime dimensions.

The first paragraph of the Crisford-Santos paper says:

...In higher dimensions, there is abundant numerical evidence that this is possible, so that this version of the WCCC does not hold [2–6]. However, in all of the previous scenarios, one starts with an unstable black hole solution, and it is far from clear whether such a black hole can be formed in the first place. The example we provide in this letter is four-dimensional and starts in the vacuum of the theory.

You can see that they reminded the reader that lots of evidence has existed that Penrose's conjecture – even the weakened one – was incorrect. But the counterexamples required more than four spacetime dimensions and non-vacuum initial conditions that someone could have argued to be forbidden by themselves. Crisford and Santos have increased the evidence against the validity of the cosmic censorship conjecture by finding a counterexample in \(D=4\); and one in which the initial state is the vacuum.

So if there is a real logical propagation of credibility between the Weak Gravity Conjecture and the Cosmic Censorship Conjecture, it goes exactly in the opposite direction than Wolchover wrote, namely:

This alliance between the Weak Gravity Conjecture and Cosmic Censorship Conjecture seems to imply that the Weak Gravity Conjecture that is backed by stronger and less ambiguous body of positive evidence helps us to conclude that despite the counterexamples, there is a sense or there are situations in which the embattled conjecture among the two, the Cosmic Censorship Conjecture, is valid, assuming inequalities that are guaranteed by the consistency of a quantum theory of gravity.

You see that it's substantially different from the stuff that Wolchover wrote.

Also, you may view the Cosmic Censorship Conjecture as a personal asset of Roger Penrose. You may ask him the following question:

By the cosmic censorship conjecture(s), do you mean that the naked singularities are avoided in general theories in which Einstein's general relativity is coupled to other fields, or are they avoided just when you impose inequalities that can only be guaranteed if one insists that the physical theory is a part of string theory?

Guess what Penrose would answer. He has unsuccessfully attempted to dismiss string theory as "fashion" so of course he would say that his conjecture shouldn't depend on string theory. But with this definition of (any) cosmic censorship conjecture, it's just wrong. This is what Crisford and Santos have shown. So the claim that this conjecture of Penrose's is more established than ours is just self-evident rubbish.

At the end, all these things are so obvious and you often need to read just the first paragraph of each relevant paper to get these things straight. However, the popular media still tend to write lots of things that are just upside down or otherwise completely wrong. Needless to say, while I have mentioned Lidice, Poles are more likely to mention the track record of German-administered villages such as Auschwitz and Birkenau.